light and sound travel speed

• Speed Of Sound vs Speed Of Light

The speed of sound and the speed of light are two common concepts that most of us likely learn about at some point in life. Both are defined rather simply, with the speed of sound being the speed that sound travels, and the speed of light being the speed at which light travels. Although these two concepts may sound similar, they are in fact radically different from one another. What are some of the differences between them?

The first notable difference between the speed of sound and light is how fast they are. In Earth’s atmosphere , the speed of sound averages at about 761-miles per hour (1,225-kilometres per hour). That may seem fast, yet when compared to the speed of light, it seems quite small. Light travels at a staggering 670-million miles per hour (1.07-billion kilometres per hour). That’s around 880,000 times faster than the speed of sound. 

Sound Must Have A Medium

In order for sound to exist, it must have a medium to travel through. For sound, this medium is air, and that’s why sound does not exist in the emptiness of space. Meanwhile, light does not need a medium to exist. Rather, light travels independently of any medium, and thus it can travel through space, unlike sound. 

The Speed Of Light Is Constant

Another notable difference between light and sound is that the speed of light is constant while the speed of sound is not. Since the speed of sound requires air to exist, its speed is dependent upon the density and temperature of air. For example, when we say that sound travels at 761-miles per hour, this is only the case at sea level and when temperatures are around 59-degrees Fahrenheit (15-degrees Celsius). If you are at a higher elevation where the density of air is lower and temperatures are colder, the speed of sound will be different. Thus, the speed of sound varies. Light, however, has no such constraint. Rather, the speed of light is constant regardless of any other factor. No matter the conditions, it always travels at the same speed. 

Things That Can Move Faster Than Sound

The speed of sound is fast, yet it is by no means the fastest thing in the universe. It is not even the fastest thing on Earth . Human’s have broken the sound barrier countless times, a speed known as supersonic speed. Light is a different story, however. The speed of light is a fixed law of nature, and it represents the fastest possible speed anything can move at. No matter how hard we try or how advanced technology becomes, the current understanding of the cosmos is that the light barrier cannot be broken. Thus, the speed of light is like a cosmic speed limit. 

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Why does light travel faster than sound?

Asked by: Toby Graham, Shrewsbury

Robert Matthews

According to Einstein's Special Relativity, the speed of light has a unique status: it's a fundamental feature of our Universe, representing the maximum speed at which information can travel from place to place. As such, nothing can match the 300,000km/s achieved by light travelling through a vacuum – least of all sound, which being waves of compression and expansion in a substance doesn’t even exist in a vacuum.

That said, light can be slowed down by being passed through transparent materials – by around 33 per cent in the case of glass. Even so, it still zooms through glass around 50,000 times faster than sound waves.

• Does the speed of light ever change?
• What would you see if you could travel at the speed of light?
• How fast does sound travel through water?
• Does sound travel further on foggy days?

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Common entrance science revision.

Light and Sound

• The Earth in Space
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Light and sound are made of WAVES. They are both forms of ENERGY.

Light travels much faster than sound. This is why the flash of lightening is seen long before the sound of thunder is heard, even though they are formed at the same instant.

Speed of light 3×10 10 m/s (300,000 km/s) Speed of sound 330m/s

Light Light is given out from a luminous source eg the sun or a projector lamp.

Light travels in straight lines.

In order to see anything light has to be reflected off of it and enter our eye.

Shadows are formed when RAYS of light are stopped by an object that does not TRANSMIT light.

When light hits some coloured paper (eg a red book) some colours are absorbed but the red light is scattered which is why the book looks red.

Words you need to know from this topic REFLECTION When light bounces off a smooth surface (eg a mirror) and forms an image behind it.

REFRACTION When light gets bent by passing from air into water or glass (or passing back again).

ABSORPTION When light hits an object and does not get reflected back (eg when light hits a piece of black paper it is absorbed, this is why the paper looks black)

TRANSMISSION When light passes straight through something like a piece of transparent paper.

DISPERSION The splitting of white light into a SPECTRUM. This is often done by a using a PRISM

FIBRE OPTICS: Optical fibres are strands of thin glass. Light can bounce from one end of the strand and come out of the other.

They are used in communications where they are now used to carry telephone or computer messages instead of wires.

Some ray diagrams

Sound        

In order to produce a sound something has to vibrate .

The vibrating object causes compressions in the air which in turn cause the ear drum in our ear to vibrate.

The frequency of the vibrations determine the pitch of the note: Faster vibrations produce a note with a higher pitch.

The size (amplitude) of the vibrations determine the volume of the sound: If the amplitude increases then the sound will get louder .

Sound travels faster in solids and liquids than it does in air.

Sound will NOT travel through a vacuum.

How sound is produced in different musical instruments

instrument part which vibrates instrument part which vibrates

Trumpet: Lips Organ: Air

Clarinet: Reed Guitar: Strings

Piano: Strings Drum: drum skin

Echoes An echo is heard when sound is reflected off a distant object.

Sonar make use of echoes to measure the distance (or shape) of an object (eg the sea floor).

It does this by measuring the length of time it takes to hear the echo.

Ultrasound Ultra sound is too high for us to hear (maybe about 40kHz). It is used to produce pictures of unborn babies,

in burglar alarms and also in some cleaning devices

Words to know:

Frequency: the number of vibrations per second.

Pitch: how high or low a note sounds.

Amplitude: the height of a wave

Volume: How loud a note is.

If the frequency increases then the pitch will increase. If the amplitude increases then the volume will increase.

Some waveforms

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What is the speed of light? Here’s the history, discovery of the cosmic speed limit

On one hand, the speed of light is just a number: 299,792,458 meters per second. And on the other, it’s one of the most important constants that appears in nature and defines the relationship of causality itself.

As far as we can measure, it is a constant. It is the same speed for every observer in the entire universe. This constancy was first established in the late 1800’s with the experiments of Albert Michelson and Edward Morley at Case Western Reserve University . They attempted to measure changes in the speed of light as the Earth orbited around the Sun. They found no such variation, and no experiment ever since then has either.

Observations of the cosmic microwave background, the light released when the universe was 380,000 years old, show that the speed of light hasn’t measurably changed in over 13.8 billion years.

In fact, we now define the speed of light to be a constant, with a precise speed of 299,792,458 meters per second. While it remains a remote possibility in deeply theoretical physics that light may not be a constant, for all known purposes it is a constant, so it’s better to just define it and move on with life.

How was the speed of light first measured?

In 1676 the Danish astronomer Ole Christensen Romer made the first quantitative measurement of how fast light travels. He carefully observed the orbit of Io, the innermost moon of Jupiter. As the Earth circles the Sun in its own orbit, sometimes it approaches Jupiter and sometimes it recedes away from it. When the Earth is approaching Jupiter, the path that light has to travel from Io is shorter than when the Earth is receding away from Jupiter. By carefully measuring the changes to Io’s orbital period, Romer calculated a speed of light of around 220,000 kilometers per second.

Observations continued to improve until by the 19 th century astronomers and physicists had developed the sophistication to get very close to the modern value. In 1865, James Clerk Maxwell made a remarkable discovery. He was investigating the properties of electricity and magnetism, which for decades had remained mysterious in unconnected laboratory experiments around the world. Maxwell found that electricity and magnetism were really two sides of the same coin, both manifestations of a single electromagnetic force.

As Maxwell explored the consequences of his new theory, he found that changing magnetic fields can lead to changing electric fields, which then lead to a new round of changing magnetic fields. The fields leapfrog over each other and can even travel through empty space. When Maxwell went to calculate the speed of these electromagnetic waves, he was surprised to see the speed of light pop out – the first theoretical calculation of this important number.

What is the most precise measurement of the speed of light?

Because it is defined to be a constant, there’s no need to measure it further. The number we’ve defined is it, with no uncertainty, no error bars. It’s done. But the speed of light is just that – a speed. The number we choose to represent it depends on the units we use: kilometers versus miles, seconds versus hours, and so on. In fact, physicists commonly just set the speed of light to be 1 to make their calculations easier. So instead of trying to measure the speed light travels, physicists turn to more precisely measuring other units, like the length of the meter or the duration of the second. In other words, the defined value of the speed of light is used to establish the length of other units like the meter.

How does light slow down?

Yes, the speed of light is always a constant. But it slows down whenever it travels through a medium like air or water. How does this work? There are a few different ways to present an answer to this question, depending on whether you prefer a particle-like picture or a wave-like picture.

In a particle-like picture, light is made of tiny little bullets called photons. All those photons always travel at the speed of light, but as light passes through a medium those photons get all tangled up, bouncing around among all the molecules of the medium. This slows down the overall propagation of light, because it takes more time for the group of photons to make it through.

In a wave-like picture, light is made of electromagnetic waves. When these waves pass through a medium, they get all the charged particles in motion, which in turn generate new electromagnetic waves of their own. These interfere with the original light, forcing it to slow down as it passes through.

Either way, light always travels at the same speed, but matter can interfere with its travel, making it slow down.

Why is the speed of light important?

The speed of light is important because it’s about way more than, well, the speed of light. In the early 1900’s Einstein realized just how special this speed is. The old physics, dominated by the work of Isaac Newton, said that the universe had a fixed reference frame from which we could measure all motion. This is why Michelson and Morley went looking for changes in the speed, because it should change depending on our point of view. But their experiments showed that the speed was always constant, so what gives?

Einstein decided to take this experiment at face value. He assumed that the speed of light is a true, fundamental constant. No matter where you are, no matter how fast you’re moving, you’ll always see the same speed.

This is wild to think about. If you’re traveling at 99% the speed of light and turn on a flashlight, the beam will race ahead of you at…exactly the speed of light, no more, no less. If you’re coming from the opposite direction, you’ll still also measure the exact same speed.

This constancy forms the basis of Einstein’s special theory of relativity, which tells us that while all motion is relative – different observers won’t always agree on the length of measurements or the duration of events – some things are truly universal, like the speed of light.

Can you go faster than light speed?

Nope. Nothing can. Any particle with zero mass must travel at light speed. But anything with mass (which is most of the universe) cannot. The problem is relativity. The faster you go, the more energy you have. But we know from Einstein’s relativity that energy and mass are the same thing. So the more energy you have, the more mass you have, which makes it harder for you to go even faster. You can get as close as you want to the speed of light, but to actually crack that barrier takes an infinite amount of energy. So don’t even try.

How is the speed at which light travels related to causality?

If you think you can find a cheat to get around the limitations of light speed, then I need to tell you about its role in special relativity. You see, it’s not just about light. It just so happens that light travels at this special speed, and it was the first thing we discovered to travel at this speed. So it could have had another name. Indeed, a better name for this speed might be “the speed of time.”

Related: Is time travel possible? An astrophysicist explains

We live in a universe of causes and effects. All effects are preceded by a cause, and all causes lead to effects. The speed of light limits how quickly causes can lead to effects. Because it’s a maximum speed limit for any motion or interaction, in a given amount of time there’s a limit to what I can influence. If I want to tap you on the shoulder and you’re right next to me, I can do it right away. But if you’re on the other side of the planet, I have to travel there first. The motion of me traveling to you is limited by the speed of light, so that sets how quickly I can tap you on the shoulder – the speed light travels dictates how quickly a single cause can create an effect.

The ability to go faster than light would allow effects to happen before their causes. In essence, time travel into the past would be possible with faster-than-light travel. Since we view time as the unbroken chain of causes and effects going from the past to the future, breaking the speed of light would break causality, which would seriously undermine our sense of the forward motion of time.

Why does light travel at this speed?

No clue. It appears to us as a fundamental constant of nature. We have no theory of physics that explains its existence or why it has the value that it does. We hope that a future understanding of nature will provide this explanation, but right now all investigations are purely theoretical. For now, we just have to take it as a given.

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How Chandra’s clear, sharp photos help study supermassive black holes

Is Pluto a planet? It depends.

‘This planet should not be there.’ Second lightest exoplanet known to date surprises astronomers

What it means for planets to align

Euclid’s new portraits of the dark universe are filled with detail, and wonder

Starmus VII hit all the right notes from beginning to end

Blue Sky Science: Why is light faster than sound?

Molly Torinus

Why is light faster than sound?

Brandon Walker

Light and sound are very different. Sound is actually a mechanical disturbance through air or another medium. Sound always needs a medium to travel through and the type of medium determines its speed.

Imagine a bunch of molecules bouncing around in the air. If you hit an object or make a fast motion, the molecules that you push are going to hit the ones in front of it. You’ll get this disturbance in the direction of travel of however you made the initial motion, and it will move through the medium. That’s how sound travels—as a pressure wave.

Light, on the other hand, is not a pressure wave—it’s a fundamental particle. One ray of light is typically called a photon, and it’s an electromagnetic disturbance. Light doesn’t need a medium to travel.

The speed of sound through air is about 340 meters per second. It’s faster through water and it’s even faster through steel. Light will travel through a vacuum at 300 million meters per second. So they’re totally different scales.

No information can propagate faster than the speed of light. If you have light that’s going through a media, it can travel slower than that. But the speed of sound and speed of light are totally incomparable.

You normally don’t notice this speed difference on a day-to-day basis. This speed difference does become apparent, for example, with lightning. You’ll always see lightning before you hear it, because typically lightning will be a mile away, two miles away. That’s a great enough distance that that speed difference becomes apparent to your brain.

14.1 Speed of Sound, Frequency, and Wavelength

Section learning objectives.

By the end of this section, you will be able to do the following:

• Relate the characteristics of waves to properties of sound waves
• Describe the speed of sound and how it changes in various media
• Relate the speed of sound to frequency and wavelength of a sound wave

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (A) examine and describe oscillatory motion and wave propagation in various types of media;
• (B) investigate and analyze characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate using the relationship between wave speed, frequency, and wavelength;
• (C) compare characteristics and behaviors of transverse waves, including electromagnetic waves and the electromagnetic spectrum, and characteristics and behaviors of longitudinal waves, including sound waves;
• (F) describe the role of wave characteristics and behaviors in medical and industrial applications.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Waves, as well as the following standards:

• (B) investigate and analyze characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate using the relationship between wave speed, frequency, and wavelength.

Section Key Terms

[BL] [OL] Review waves and types of waves—mechanical and non-mechanical, transverse and longitudinal, pulse and periodic. Review properties of waves—amplitude, period, frequency, velocity and their inter-relations.

Properties of Sound Waves

Sound is a wave. More specifically, sound is defined to be a disturbance of matter that is transmitted from its source outward. A disturbance is anything that is moved from its state of equilibrium. Some sound waves can be characterized as periodic waves, which means that the atoms that make up the matter experience simple harmonic motion .

A vibrating string produces a sound wave as illustrated in Figure 14.2 , Figure 14.3 , and Figure 14.4 . As the string oscillates back and forth, part of the string’s energy goes into compressing and expanding the surrounding air. This creates slightly higher and lower pressures. The higher pressure... regions are compressions, and the low pressure regions are rarefactions . The pressure disturbance moves through the air as longitudinal waves with the same frequency as the string. Some of the energy is lost in the form of thermal energy transferred to the air. You may recall from the chapter on waves that areas of compression and rarefaction in longitudinal waves (such as sound) are analogous to crests and troughs in transverse waves .

The amplitude of a sound wave decreases with distance from its source, because the energy of the wave is spread over a larger and larger area. But some of the energy is also absorbed by objects, such as the eardrum in Figure 14.5 , and some of the energy is converted to thermal energy in the air. Figure 14.4 shows a graph of gauge pressure versus distance from the vibrating string. From this figure, you can see that the compression of a longitudinal wave is analogous to the peak of a transverse wave, and the rarefaction of a longitudinal wave is analogous to the trough of a transverse wave. Just as a transverse wave alternates between peaks and troughs, a longitudinal wave alternates between compression and rarefaction.

The Speed of Sound

[BL] Review the fact that sound is a mechanical wave and requires a medium through which it is transmitted.

[OL] [AL] Ask students if they know the speed of sound and if not, ask them to take a guess. Ask them why the sound of thunder is heard much after the lightning is seen during storms. This phenomenon is also observed during a display of fireworks. Through this discussion, develop the concept that the speed of sound is finite and measurable and is much slower than that of light.

The speed of sound varies greatly depending upon the medium it is traveling through. The speed of sound in a medium is determined by a combination of the medium’s rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound. The greater the density of a medium, the slower the speed of sound. The speed of sound in air is low, because air is compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases. Table 14.1 shows the speed of sound in various media. Since temperature affects density, the speed of sound varies with the temperature of the medium through which it’s traveling to some extent, especially for gases.

Misconception Alert

Students might be confused between rigidity and density and how they affect the speed of sound. The speed of sound is slower in denser media. Solids are denser than gases. However, they are also very rigid, and hence sound travels faster in solids. Stress on the fact that the speed of sound always depends on a combination of these two properties of any medium.

[BL] Note that in the table, the speed of sound in very rigid materials such as glass, aluminum, and steel ... is quite high, whereas the speed in rubber, which is considerably less rigid, is quite low.

The Relationship Between the Speed of Sound and the Frequency and Wavelength of a Sound Wave

Sound, like all waves, travels at certain speeds through different media and has the properties of frequency and wavelength . Sound travels much slower than light—you can observe this while watching a fireworks display (see Figure 14.6 ), since the flash of an explosion is seen before its sound is heard.

The relationship between the speed of sound, its frequency, and wavelength is the same as for all waves:

where v is the speed of sound (in units of m/s), f is its frequency (in units of hertz), and λ λ is its wavelength (in units of meters). Recall that wavelength is defined as the distance between adjacent identical parts of a wave. The wavelength of a sound, therefore, is the distance between adjacent identical parts of a sound wave. Just as the distance between adjacent crests in a transverse wave is one wavelength, the distance between adjacent compressions in a sound wave is also one wavelength, as shown in Figure 14.7 . The frequency of a sound wave is the same as that of the source. For example, a tuning fork vibrating at a given frequency would produce sound waves that oscillate at that same frequency. The frequency of a sound is the number of waves that pass a point per unit time.

[BL] [OL] [AL] In musical instruments, shorter strings vibrate faster and hence produce sounds at higher pitches. Fret placements on instruments such as guitars, banjos, and mandolins, are mathematically determined to give the correct interval or change in pitch. When the string is pushed against the fret wire, the string is effectively shortened, changing its pitch. Ask students to experiment with strings of different lengths and observe how the pitch changes in each case.

One of the more important properties of sound is that its speed is nearly independent of frequency. If this were not the case, and high-frequency sounds traveled faster, for example, then the farther you were from a band in a football stadium, the more the sound from the low-pitch instruments would lag behind the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, and so all frequencies must travel at nearly the same speed.

Recall that v = f λ v = f λ , and in a given medium under fixed temperature and humidity, v is constant. Therefore, the relationship between f and λ λ is inverse: The higher the frequency, the shorter the wavelength of a sound wave.

Teacher Demonstration

Hold a meter stick flat on a desktop, with about 80 cm sticking out over the edge of the desk. Make the meter stick vibrate by pulling the tip down and releasing, while holding the meter stick tight to the desktop. While it is vibrating, move the stick back onto the desktop, shortening the part that is sticking out. Students will see the shortening of the vibrating part of the meter stick, and hear the pitch or number of vibrations go up—an increase in frequency.

The speed of sound can change when sound travels from one medium to another. However, the frequency usually remains the same because it is like a driven oscillation and maintains the frequency of the original source. If v changes and f remains the same, then the wavelength λ λ must change. Since v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.

[AL] Ask students to predict what would happen if the speeds of sound in air varied by frequency.

Virtual Physics

This simulation lets you see sound waves. Adjust the frequency or amplitude (volume) and you can see and hear how the wave changes. Move the listener around and hear what she hears. Switch to the Two Source Interference tab or the Interference by Reflection tab to experiment with interference and reflection.

Tips For Success

Make sure to have audio enabled and set to Listener rather than Speaker, or else the sound will not vary as you move the listener around.

• Because, intensity of the sound wave changes with the frequency.
• Because, the speed of the sound wave changes when the frequency is changed.
• Because, loudness of the sound wave takes time to adjust after a change in frequency.
• Because it takes time for sound to reach the listener, so the listener perceives the new frequency of sound wave after a delay.
• Yes, the speed of propagation depends only on the frequency of the wave.
• Yes, the speed of propagation depends upon the wavelength of the wave, and wavelength changes as the frequency changes.
• No, the speed of propagation depends only on the wavelength of the wave.
• No, the speed of propagation is constant in a given medium; only the wavelength changes as the frequency changes.

Voice as a Sound Wave

In this lab you will observe the effects of blowing and speaking into a piece of paper in order to compare and contrast different sound waves.

• sheet of paper

Instructions

• Suspend a sheet of paper so that the top edge of the paper is fixed and the bottom edge is free to move. You could tape the top edge of the paper to the edge of a table, for example.
• Gently blow air near the edge of the bottom of the sheet and note how the sheet moves.
• Speak softly and then louder such that the sounds hit the edge of the bottom of the paper, and note how the sheet moves.
• Interpret the results.

Grasp Check

Which sound wave property increases when you are speaking more loudly than softly?

• amplitude of the wave
• frequency of the wave
• speed of the wave
• wavelength of the wave

Worked Example

What are the wavelengths of audible sounds.

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in conditions where sound travels at 348.7 m/s.

To find wavelength from frequency, we can use v = f λ v = f λ .

(1) Identify the knowns. The values for v and f are given.

(2) Solve the relationship between speed, frequency and wavelength for λ λ .

(3) Enter the speed and the minimum frequency to give the maximum wavelength.

(4) Enter the speed and the maximum frequency to give the minimum wavelength.

Because the product of f multiplied by λ λ equals a constant velocity in unchanging conditions, the smaller f is, the larger λ λ must be, and vice versa. Note that you can also easily rearrange the same formula to find frequency or velocity.

Practice Problems

• 5 × 10 3 m / s
• 3.2 × 10 2 m / s
• 2 × 10 − 4 m/s
• 8 × 10 2 m / s
• 2.0 × 10 7 m
• 1.5 × 10 7 m
• 1.4 × 10 2 m
• 7.4 × 10 − 3 m

Links To Physics

Echolocation.

Echolocation is the use of reflected sound waves to locate and identify objects. It is used by animals such as bats, dolphins and whales, and is also imitated by humans in SONAR—Sound Navigation and Ranging—and echolocation technology.

Bats, dolphins and whales use echolocation to navigate and find food in their environment. They locate an object (or obstacle) by emitting a sound and then sensing the reflected sound waves. Since the speed of sound in air is constant, the time it takes for the sound to travel to the object and back gives the animal a sense of the distance between itself and the object. This is called ranging . Figure 14.8 shows a bat using echolocation to sense distances.

Echolocating animals identify an object by comparing the relative intensity of the sound waves returning to each ear to figure out the angle at which the sound waves were reflected. This gives information about the direction, size and shape of the object. Since there is a slight distance in position between the two ears of an animal, the sound may return to one of the ears with a bit of a delay, which also provides information about the position of the object. For example, if a bear is directly to the right of a bat, the echo will return to the bat’s left ear later than to its right ear. If, however, the bear is directly ahead of the bat, the echo would return to both ears at the same time. For an animal without a sense of sight such as a bat, it is important to know where other animals are as well as what they are; their survival depends on it.

Principles of echolocation have been used to develop a variety of useful sensing technologies. SONAR, is used by submarines to detect objects underwater and measure water depth. Unlike animal echolocation, which relies on only one transmitter (a mouth) and two receivers (ears), manmade SONAR uses many transmitters and beams to get a more accurate reading of the environment. Radar technologies use the echo of radio waves to locate clouds and storm systems in weather forecasting, and to locate aircraft for air traffic control. Some new cars use echolocation technology to sense obstacles around the car, and warn the driver who may be about to hit something (or even to automatically parallel park). Echolocation technologies and training systems are being developed to help visually impaired people navigate their everyday environments.

• The echo would return to the left ear first.
• The echo would return to the right ear first.

Check Your Understanding

Use these questions to assess student achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify which and direct students to the relevant content.

• Rarefaction is the high-pressure region created in a medium when a longitudinal wave passes through it.
• Rarefaction is the low-pressure region created in a medium when a longitudinal wave passes through it.
• Rarefaction is the highest point of amplitude of a sound wave.
• Rarefaction is the lowest point of amplitude of a sound wave.

What sort of motion do the particles of a medium experience when a sound wave passes through it?

• Simple harmonic motion
• Circular motion
• Random motion
• Translational motion

What does the speed of sound depend on?

• The wavelength of the wave
• The size of the medium
• The frequency of the wave
• The properties of the medium

What property of a gas would affect the speed of sound traveling through it?

• The volume of the gas
• The flammability of the gas
• The mass of the gas
• The compressibility of the gas

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• Authors: Paul Peter Urone, Roger Hinrichs
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• Book title: Physics
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June 9, 2003

How were the speed of sound and the speed of light determined and measured?

Chris Oates, a physicist in the Time and Frequency Division of the National Institute of Standards and Technology (NIST), explains.

Despite the differences between light and sound, the same two basic methods have been used in most measurements of their respective speeds. The first method is based on simply measuring the time it takes a pulse of light or sound to traverse a known distance; dividing the distance by the transit time then gives the speed. The second method makes use of the wave nature common to these phenomena: by measuring both the frequency (f) and the wavelength () of the propagating wave, one can derive the speed of the wave from the simple wave relation, speed = f×. (The frequency of a wave is the number of crests that pass per second, whereas the wavelength is the distance between crests). Although the two phenomena share these measurement approaches, the fundamental differences between light and sound have led to very different experimental implementations, as well as different historical developments, in the determination of their speeds.

In its simplest form, sound can be thought of as a longitudinal wave consisting of compressions and extensions of a medium along the direction of propagation. Because sound requires a medium through which to propagate, the speed of a sound wave is determined by the properties of the medium itself (such as density, stiffness, and temperature). These parameters thus need to be included in any reported measurements. In fact, one can turn such measurements around and actually use them to determine thermodynamic properties of the medium (the ratio of specific heats, for example).

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The first known theoretical treatise on sound was provided by Sir Isaac Newton in his Principia, which predicted a value for the speed of sound in air that differs by about 16 percent from the currently accepted value. Early experimental values were based on measurements of the time it took the sound of cannon blasts to cover a given distance and were good to better than 1 percent of the currently accepted value of 331.5 m/s at 0 degrees Celsius. Daniel Colladon and Charles-Francois Sturm first performed similar measurements in water in Lake Geneva in 1826. They found a value only 0.2 percent below the currently accepted value of ~1,440 m/s at 8 degrees C. These measurements all suffered from variations in the media themselves over long distances, so most subsequent determinations have been performed in the laboratory, where environmental parameters could be better controlled, and a larger variety of gases and liquids could be investigated. These experiments often use tubes of gas or liquid (or bars of solid material) with precisely calibrated lengths. One can then derive the speed of sound from a measurement of the time that an impulse of sound takes to traverse the tube. Alternatively (and usually more accurately), one can excite resonant frequencies of the tube (much like those of a flute) by inducing a vibration at one end with a loudspeaker, tuning fork, or other type of transducer. Because the corresponding resonant wavelengths have a simple relationship to the tube length, one can then determine the speed of sound from the wave relation and make corrections for tube geometry for comparisons with speeds in free space.

The wave nature of light is quite different from that of sound. In its simplest form, an electromagnetic wave (such as light, radio, or microwave) is transverse, consisting of oscillating electric and magnetic fields that are perpendicular to the direction of propagation. Moreover, although the medium through which light travels does affect its speed (reducing it by the index of refraction of the material), light can also travel through a vacuum, thus providing a unique context for defining its speed. In fact, the speed of light in a vacuum, c, is a fundamental building block of Einstein's theory of relativity, because it sets the upper limit for speeds in the universe. As a result, it appears in a wide range of physical formulae, perhaps the most famous of which is E=mc 2 . The speed of light can thus be measured in a variety of ways, but due to its extremely high value (~300,000 km/s or 186,000 mi/s), it was initially considerably harder to measure than the speed of sound. Early efforts such as Galileo's pair of observers sitting on opposing hills flashing lanterns back and forth lacked the technology needed to measure accurately the transit times of only a few microseconds. Remarkably, astronomical observations in the 18th century led to a determination of the speed of light with an uncertainty of only 1 percent. Better measurements, however, required a laboratory environment. Louis Fizeau and Leon Foucault were able to perform updated versions of Galileo¿s experiment through the use of ingenious combinations of rotating mirrors (along with improved measurement technology) and they made a series of beautiful measurements of the speed of light. With still further improvements, Albert A. Michelson performed measurements good to nearly one part in ten thousand.

Metrology of the speed of light changed dramatically with a determination made here at NIST in 1972. This measurement was based on a helium-neon laser whose frequency was fixed by a feedback loop to match the frequency corresponding to the splitting between two quantized energy levels of the methane molecule. Both the frequency and wavelength of this highly stable laser were accurately measured, thereby leading to a 100-times reduction in the uncertainty for the value of the speed of light. This measurement and subsequent measurements based on other atomic/molecular standards were limited not by the measurement technique, but by uncertainties in the definition of the meter itself. Because it was clear that future measurements would be similarly limited, the 17th Conf¿rence G¿n¿rale des Poids et Mesures (General Conference on Weights and Measures) decided in 1983 to redefine the meter in terms of the speed of light. The speed of light thus became a constant (defined to be 299,792,458 m/s), never to be measured again. As a result, the definition of the meter is directly linked (via the relation c= f×) to that of frequency, which is by far the most accurately measured physical quantity (presently the best cesium atomic fountain clocks have a fractional frequency uncertainty of about 1x10 -15 ).

What is the speed of light?

The speed of light is the speed limit of the universe. Or is it?

What is a light-year?

• Speed of light FAQs
• Special relativity
• Faster than light
• Slowing down light
• Faster-than-light travel

Bibliography

The speed of light traveling through a vacuum is exactly 299,792,458 meters (983,571,056 feet) per second. That's about 186,282 miles per second — a universal constant known in equations as "c," or light speed. 

According to physicist Albert Einstein 's theory of special relativity , on which much of modern physics is based, nothing in the universe can travel faster than light. The theory states that as matter approaches the speed of light, the matter's mass becomes infinite. That means the speed of light functions as a speed limit on the whole universe . The speed of light is so immutable that, according to the U.S. National Institute of Standards and Technology , it is used to define international standard measurements like the meter (and by extension, the mile, the foot and the inch). Through some crafty equations, it also helps define the kilogram and the temperature unit Kelvin .

But despite the speed of light's reputation as a universal constant, scientists and science fiction writers alike spend time contemplating faster-than-light travel. So far no one's been able to demonstrate a real warp drive, but that hasn't slowed our collective hurtle toward new stories, new inventions and new realms of physics.

Related: Special relativity holds up to a high-energy test

A l ight-year is the distance that light can travel in one year — about 6 trillion miles (10 trillion kilometers). It's one way that astronomers and physicists measure immense distances across our universe.

Light travels from the moon to our eyes in about 1 second, which means the moon is about 1 light-second away. Sunlight takes about 8 minutes to reach our eyes, so the sun is about 8 light minutes away. Light from Alpha Centauri , which is the nearest star system to our own, requires roughly 4.3 years to get here, so Alpha Centauri is 4.3 light-years away.

"To obtain an idea of the size of a light-year, take the circumference of the Earth (24,900 miles), lay it out in a straight line, multiply the length of the line by 7.5 (the corresponding distance is one light-second), then place 31.6 million similar lines end to end," NASA's Glenn Research Center says on its website . "The resulting distance is almost 6 trillion (6,000,000,000,000) miles!"

Stars and other objects beyond our solar system lie anywhere from a few light-years to a few billion light-years away. And everything astronomers "see" in the distant universe is literally history. When astronomers study objects that are far away, they are seeing light that shows the objects as they existed at the time that light left them. 

This principle allows astronomers to see the universe as it looked after the Big Bang , which took place about 13.8 billion years ago. Objects that are 10 billion light-years away from us appear to astronomers as they looked 10 billion years ago — relatively soon after the beginning of the universe — rather than how they appear today.

Related: Why the universe is all history

Speed of light FAQs answered by an expert

We asked Rob Zellem, exoplanet-hunter and staff scientist at NASA's Jet Propulsion Lab, a few frequently asked questions about the speed of light. 

Dr. Rob Zellem is a staff scientist at NASA's Jet Propulsion Laboratory, a federally funded research and development center operated by the California Institute of Technology. Rob is the project lead for Exoplanet Watch, a citizen science project to observe exoplanets, planets outside of our own solar system, with small telescopes. He is also the Science Calibration lead for the Nancy Grace Roman Space Telescope's Coronagraph Instrument, which will directly image exoplanets. 

What is faster than the speed of light?

Nothing! Light is a "universal speed limit" and, according to Einstein's theory of relativity, is the fastest speed in the universe: 300,000 kilometers per second (186,000 miles per second). 

Is the speed of light constant?

The speed of light is a universal constant in a vacuum, like the vacuum of space. However, light *can* slow down slightly when it passes through an absorbing medium, like water (225,000 kilometers per second = 140,000 miles per second) or glass (200,000 kilometers per second = 124,000 miles per second). 

Who discovered the speed of light?

One of the first measurements of the speed of light was by Rømer in 1676 by observing the moons of Jupiter . The speed of light was first measured to high precision in 1879 by the Michelson-Morley Experiment. 

How do we know the speed of light?

Rømer was able to measure the speed of light by observing eclipses of Jupiter's moon Io. When Jupiter was closer to Earth, Rømer noted that eclipses of Io occurred slightly earlier than when Jupiter was farther away. Rømer attributed this effect due the time it takes for light to travel over the longer distance when Jupiter was farther from the Earth. 

How did we learn the speed of light?

As early as the 5th century BC, Greek philosophers like Empedocles and Aristotle disagreed on the nature of light speed. Empedocles proposed that light, whatever it was made of, must travel and therefore, must have a rate of travel. Aristotle wrote a rebuttal of Empedocles' view in his own treatise, On Sense and the Sensible , arguing that light, unlike sound and smell, must be instantaneous. Aristotle was wrong, of course, but it would take hundreds of years for anyone to prove it. 

In the mid 1600s, the Italian astronomer Galileo Galilei stood two people on hills less than a mile apart. Each person held a shielded lantern. One uncovered his lantern; when the other person saw the flash, he uncovered his too. But Galileo's experimental distance wasn't far enough for his participants to record the speed of light. He could only conclude that light traveled at least 10 times faster than sound.

In the 1670s, Danish astronomer Ole Rømer tried to create a reliable timetable for sailors at sea, and according to NASA , accidentally came up with a new best estimate for the speed of light. To create an astronomical clock, he recorded the precise timing of the eclipses of Jupiter's moon , Io, from Earth . Over time, Rømer observed that Io's eclipses often differed from his calculations. He noticed that the eclipses appeared to lag the most when Jupiter and Earth were moving away from one another, showed up ahead of time when the planets were approaching and occurred on schedule when the planets were at their closest or farthest points. This observation demonstrated what we today know as the Doppler effect, the change in frequency of light or sound emitted by a moving object that in the astronomical world manifests as the so-called redshift , the shift towards "redder", longer wavelengths in objects speeding away from us. In a leap of intuition, Rømer determined that light was taking measurable time to travel from Io to Earth. 

Rømer used his observations to estimate the speed of light. Since the size of the solar system and Earth's orbit wasn't yet accurately known, argued a 1998 paper in the American Journal of Physics , he was a bit off. But at last, scientists had a number to work with. Rømer's calculation put the speed of light at about 124,000 miles per second (200,000 km/s).

In 1728, English physicist James Bradley based a new set of calculations on the change in the apparent position of stars caused by Earth's travels around the sun. He estimated the speed of light at 185,000 miles per second (301,000 km/s) — accurate to within about 1% of the real value, according to the American Physical Society .

Two new attempts in the mid-1800s brought the problem back to Earth. French physicist Hippolyte Fizeau set a beam of light on a rapidly rotating toothed wheel, with a mirror set up 5 miles (8 km) away to reflect it back to its source. Varying the speed of the wheel allowed Fizeau to calculate how long it took for the light to travel out of the hole, to the adjacent mirror, and back through the gap. Another French physicist, Leon Foucault, used a rotating mirror rather than a wheel to perform essentially the same experiment. The two independent methods each came within about 1,000 miles per second (1,609 km/s) of the speed of light.

Another scientist who tackled the speed of light mystery was Poland-born Albert A. Michelson, who grew up in California during the state's gold rush period, and honed his interest in physics while attending the U.S. Naval Academy, according to the University of Virginia . In 1879, he attempted to replicate Foucault's method of determining the speed of light, but Michelson increased the distance between mirrors and used extremely high-quality mirrors and lenses. Michelson's result of 186,355 miles per second (299,910 km/s) was accepted as the most accurate measurement of the speed of light for 40 years, until Michelson re-measured it himself. In his second round of experiments, Michelson flashed lights between two mountain tops with carefully measured distances to get a more precise estimate. And in his third attempt just before his death in 1931, according to the Smithsonian's Air and Space magazine, he built a mile-long depressurized tube of corrugated steel pipe. The pipe simulated a near-vacuum that would remove any effect of air on light speed for an even finer measurement, which in the end was just slightly lower than the accepted value of the speed of light today. 

Michelson also studied the nature of light itself, wrote astrophysicist Ethan Siegal in the Forbes science blog, Starts With a Bang . The best minds in physics at the time of Michelson's experiments were divided: Was light a wave or a particle? 

Michelson, along with his colleague Edward Morley, worked under the assumption that light moved as a wave, just like sound. And just as sound needs particles to move, Michelson and Morley and other physicists of the time reasoned, light must have some kind of medium to move through. This invisible, undetectable stuff was called the "luminiferous aether" (also known as "ether"). 

Though Michelson and Morley built a sophisticated interferometer (a very basic version of the instrument used today in LIGO facilities), Michelson could not find evidence of any kind of luminiferous aether whatsoever. Light, he determined, can and does travel through a vacuum.

"The experiment — and Michelson's body of work — was so revolutionary that he became the only person in history to have won a Nobel Prize for a very precise non-discovery of anything," Siegal wrote. "The experiment itself may have been a complete failure, but what we learned from it was a greater boon to humanity and our understanding of the universe than any success would have been!"

Special relativity and the speed of light

Einstein's theory of special relativity unified energy, matter and the speed of light in a famous equation: E = mc^2. The equation describes the relationship between mass and energy — small amounts of mass (m) contain, or are made up of, an inherently enormous amount of energy (E). (That's what makes nuclear bombs so powerful: They're converting mass into blasts of energy.) Because energy is equal to mass times the speed of light squared, the speed of light serves as a conversion factor, explaining exactly how much energy must be within matter. And because the speed of light is such a huge number, even small amounts of mass must equate to vast quantities of energy.

In order to accurately describe the universe, Einstein's elegant equation requires the speed of light to be an immutable constant. Einstein asserted that light moved through a vacuum, not any kind of luminiferous aether, and in such a way that it moved at the same speed no matter the speed of the observer. 

Think of it like this: Observers sitting on a train could look at a train moving along a parallel track and think of its relative movement to themselves as zero. But observers moving nearly the speed of light would still perceive light as moving away from them at more than 670 million mph. (That's because moving really, really fast is one of the only confirmed methods of time travel — time actually slows down for those observers, who will age slower and perceive fewer moments than an observer moving slowly.)

In other words, Einstein proposed that the speed of light doesn't vary with the time or place that you measure it, or how fast you yourself are moving. 

Therefore, objects with mass cannot ever reach the speed of light. If an object ever did reach the speed of light, its mass would become infinite. And as a result, the energy required to move the object would also become infinite: an impossibility.

That means if we base our understanding of physics on special relativity (which most modern physicists do), the speed of light is the immutable speed limit of our universe — the fastest that anything can travel. 

What goes faster than the speed of light?

Although the speed of light is often referred to as the universe's speed limit, the universe actually expands even faster. The universe expands at a little more than 42 miles (68 kilometers) per second for each megaparsec of distance from the observer, wrote astrophysicist Paul Sutter in a previous article for Space.com . (A megaparsec is 3.26 million light-years — a really long way.) 

In other words, a galaxy 1 megaparsec away appears to be traveling away from the Milky Way at a speed of 42 miles per second (68 km/s), while a galaxy two megaparsecs away recedes at nearly 86 miles per second (136 km/s), and so on. 

"At some point, at some obscene distance, the speed tips over the scales and exceeds the speed of light, all from the natural, regular expansion of space," Sutter explained. "It seems like it should be illegal, doesn't it?"

Special relativity provides an absolute speed limit within the universe, according to Sutter, but Einstein's 1915 theory regarding general relativity allows different behavior when the physics you're examining are no longer "local."

"A galaxy on the far side of the universe? That's the domain of general relativity, and general relativity says: Who cares! That galaxy can have any speed it wants, as long as it stays way far away, and not up next to your face," Sutter wrote. "Special relativity doesn't care about the speed — superluminal or otherwise — of a distant galaxy. And neither should you."

Does light ever slow down?

Light in a vacuum is generally held to travel at an absolute speed, but light traveling through any material can be slowed down. The amount that a material slows down light is called its refractive index. Light bends when coming into contact with particles, which results in a decrease in speed.

For example, light traveling through Earth's atmosphere moves almost as fast as light in a vacuum, slowing down by just three ten-thousandths of the speed of light. But light passing through a diamond slows to less than half its typical speed, PBS NOVA reported. Even so, it travels through the gem at over 277 million mph (almost 124,000 km/s) — enough to make a difference, but still incredibly fast.

Light can be trapped — and even stopped — inside ultra-cold clouds of atoms, according to a 2001 study published in the journal Nature . More recently, a 2018 study published in the journal Physical Review Letters proposed a new way to stop light in its tracks at "exceptional points," or places where two separate light emissions intersect and merge into one.

Researchers have also tried to slow down light even when it's traveling through a vacuum. A team of Scottish scientists successfully slowed down a single photon, or particle of light, even as it moved through a vacuum, as described in their 2015 study published in the journal Science . In their measurements, the difference between the slowed photon and a "regular" photon was just a few millionths of a meter, but it demonstrated that light in a vacuum can be slower than the official speed of light. 

Can we travel faster than light?

— Spaceship could fly faster than light

— Here's what the speed of light looks like in slow motion

— Why is the speed of light the way it is?

Science fiction loves the idea of "warp speed." Faster-than-light travel makes countless sci-fi franchises possible, condensing the vast expanses of space and letting characters pop back and forth between star systems with ease. 

But while faster-than-light travel isn't guaranteed impossible, we'd need to harness some pretty exotic physics to make it work. Luckily for sci-fi enthusiasts and theoretical physicists alike, there are lots of avenues to explore.

All we have to do is figure out how to not move ourselves — since special relativity would ensure we'd be long destroyed before we reached high enough speed — but instead, move the space around us. Easy, right? 

One proposed idea involves a spaceship that could fold a space-time bubble around itself. Sounds great, both in theory and in fiction.

"If Captain Kirk were constrained to move at the speed of our fastest rockets, it would take him a hundred thousand years just to get to the next star system," said Seth Shostak, an astronomer at the Search for Extraterrestrial Intelligence (SETI) Institute in Mountain View, California, in a 2010 interview with Space.com's sister site LiveScience . "So science fiction has long postulated a way to beat the speed of light barrier so the story can move a little more quickly."

Without faster-than-light travel, any "Star Trek" (or "Star War," for that matter) would be impossible. If humanity is ever to reach the farthest — and constantly expanding — corners of our universe, it will be up to future physicists to boldly go where no one has gone before.

Additional resources

For more on the speed of light, check out this fun tool from Academo that lets you visualize how fast light can travel from any place on Earth to any other. If you’re more interested in other important numbers, get familiar with the universal constants that define standard systems of measurement around the world with the National Institute of Standards and Technology . And if you’d like more on the history of the speed of light, check out the book " Lightspeed: The Ghostly Aether and the Race to Measure the Speed of Light " (Oxford, 2019) by John C. H. Spence.

Aristotle. “On Sense and the Sensible.” The Internet Classics Archive, 350AD. http://classics.mit.edu/Aristotle/sense.2.2.html .

D’Alto, Nick. “The Pipeline That Measured the Speed of Light.” Smithsonian Magazine, January 2017. https://www.smithsonianmag.com/air-space-magazine/18_fm2017-oo-180961669/ .

Fowler, Michael. “Speed of Light.” Modern Physics. University of Virginia. Accessed January 13, 2022. https://galileo.phys.virginia.edu/classes/252/spedlite.html#Albert%20Abraham%20Michelson .

Giovannini, Daniel, Jacquiline Romero, Václav Potoček, Gergely Ferenczi, Fiona Speirits, Stephen M. Barnett, Daniele Faccio, and Miles J. Padgett. “Spatially Structured Photons That Travel in Free Space Slower than the Speed of Light.” Science, February 20, 2015. https://www.science.org/doi/abs/10.1126/science.aaa3035 .

Goldzak, Tamar, Alexei A. Mailybaev, and Nimrod Moiseyev. “Light Stops at Exceptional Points.” Physical Review Letters 120, no. 1 (January 3, 2018): 013901. https://doi.org/10.1103/PhysRevLett.120.013901 . 

Hazen, Robert. “What Makes Diamond Sparkle?” PBS NOVA, January 31, 2000. https://www.pbs.org/wgbh/nova/article/diamond-science/ . 

“How Long Is a Light-Year?” Glenn Learning Technologies Project, May 13, 2021. https://www.grc.nasa.gov/www/k-12/Numbers/Math/Mathematical_Thinking/how_long_is_a_light_year.htm . 

American Physical Society News. “July 1849: Fizeau Publishes Results of Speed of Light Experiment,” July 2010. http://www.aps.org/publications/apsnews/201007/physicshistory.cfm . 

Liu, Chien, Zachary Dutton, Cyrus H. Behroozi, and Lene Vestergaard Hau. “Observation of Coherent Optical Information Storage in an Atomic Medium Using Halted Light Pulses.” Nature 409, no. 6819 (January 2001): 490–93. https://doi.org/10.1038/35054017 . 

NIST. “Meet the Constants.” October 12, 2018. https://www.nist.gov/si-redefinition/meet-constants . 

Ouellette, Jennifer. “A Brief History of the Speed of Light.” PBS NOVA, February 27, 2015. https://www.pbs.org/wgbh/nova/article/brief-history-speed-light/ . 

Shea, James H. “Ole Ro/Mer, the Speed of Light, the Apparent Period of Io, the Doppler Effect, and the Dynamics of Earth and Jupiter.” American Journal of Physics 66, no. 7 (July 1, 1998): 561–69. https://doi.org/10.1119/1.19020 . 

Siegel, Ethan. “The Failed Experiment That Changed The World.” Forbes, April 21, 2017. https://www.forbes.com/sites/startswithabang/2017/04/21/the-failed-experiment-that-changed-the-world/ . 

Stern, David. “Rømer and the Speed of Light,” October 17, 2016. https://pwg.gsfc.nasa.gov/stargaze/Sun4Adop1.htm . 

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Vicky Stein is a science writer based in California. She has a bachelor's degree in ecology and evolutionary biology from Dartmouth College and a graduate certificate in science writing from the University of California, Santa Cruz (2018). Afterwards, she worked as a news assistant for PBS NewsHour, and now works as a freelancer covering anything from asteroids to zebras. Follow her most recent work (and most recent pictures of nudibranchs) on Twitter. 

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17.3: Speed of Sound

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Learning Objectives

• Explain the relationship between wavelength and frequency of sound
• Determine the speed of sound in different media
• Derive the equation for the speed of sound in air
• Determine the speed of sound in air for a given temperature

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display (Figure \(\PageIndex{1}\)). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

The difference between the speed of light and the speed of sound can also be experienced during an electrical storm. The flash of lighting is often seen before the clap of thunder. You may have heard that if you count the number of seconds between the flash and the sound, you can estimate the distance to the source. Every five seconds converts to about one mile. The velocity of any wave is related to its frequency and wavelength by

\[v = f \lambda, \label{17.3}\]

where \(v\) is the speed of the wave, \(f\) is its frequency, and \(\lambda\) is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions (Figure \(\PageIndex{2}\)). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table \(\PageIndex{1}\) shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property, divided by the inertial property,

\[v = \sqrt{\frac{\text{elastic property}}{\text{inertial property}}} \ldotp\]

Also, sound waves satisfy the wave equation derived in Waves ,

\[\frac{\partial^{2} y (x,t)}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2} y (x,t)}{\partial t^{2}} \ldotp\]

Recall from Waves that the speed of a wave on a string is equal to \(v = \sqrt{\frac{F_{T}}{\mu}}\), where the restoring force is the tension in the string F T and the linear density \(\mu\) is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

\[v = \sqrt{\frac{B}{\rho}} \ldotp \label{17.4}\]

The speed of sound in a solid the depends on the Young’s modulus of the medium and the density,

\[v = \sqrt{\frac{Y}{\rho}} \ldotp \label{17.5}\]

In an ideal gas (see The Kinetic Theory of Gases ), the equation for the speed of sound is

\[v = \sqrt{\frac{\gamma RT_{K}}{M}}, \label{17.6}\]

where \(\gamma\) is the adiabatic index, R = 8.31 J/mol • K is the gas constant, T K is the absolute temperature in kelvins, and M is the molecular mass. In general, the more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of simple harmonic motion is directly proportional to the stiffness of the oscillating object as measured by k, the spring constant. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to m, the mass of the oscillating object. The speed of sound in air is low, because air is easily compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Because the speed of sound depends on the density of the material, and the density depends on the temperature, there is a relationship between the temperature in a given medium and the speed of sound in the medium. For air at sea level, the speed of sound is given by

\[v = 331\; m/s \sqrt{1 + \frac{T_{C}}{273 °C}} = 331\; m/s \sqrt{\frac{T_{K}}{273\; K}} \label{17.7}\]

where the temperature in the first equation (denoted as T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas,

\[v_{rms} = \sqrt{\frac{3k_{B}T}{m}}.\]

where \(k_B\) is the Boltzmann constant (1.38 x 10 −23 J/K) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas \(v_{rms}\) describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0°C , the speed of sound is 331 m/s, whereas at 20.0 °C, it is 343 m/s, less than a 4% increase. Figure \(\PageIndex{3}\) shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics . Consider fluid flow through a pipe with cross-sectional area \(A\) (Figure \(\PageIndex{4}\)). The mass in a small volume of length \(x\) of the pipe is equal to the density times the volume, or

\[m = \rho V = \rho Ax.\]

The mass flow rate is

\[\frac{dm}{dt} = \frac{d}{dt} (\rho V) = \frac{d}{dt} (\rho Ax) = \rho A \frac{dx}{dt} = \rho Av \ldotp\]

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume,

\[\rho_{in} A_{in}v_{in} = \rho_{out} A_{out}v_{out}.\]

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries (Figure \(\PageIndex{5}\)). The density, temperature, and velocity on one side of the volume of the fluid are given as \(\rho\), T, v, and on the other side are \(\rho\) + d\(\rho\), \(T + dT\), \(v + dv\).

The continuity equation states that the mass flow rate entering the volume is equal to the mass flow rate leaving the volume, so

\[\rho Av = (\rho + d \rho)A(v + dv) \ldotp\]

This equation can be simplified, noting that the area cancels and considering that the multiplication of two infinitesimals is approximately equal to zero: d\(\rho\)(dv) ≈ 0,

\[\begin{split} \rho v & = (\rho + d \rho)(v + dv) \\ & = \rho v + \rho (dv) + (d \rho)v + (d \rho)(dv) \\ 0 & = \rho (dv) + (d \rho) v \\ \rho\; dv & = -v\; d \rho \ldotp \end{split}\]

The net force on the volume of fluid (Figure \(\PageIndex{6}\)) equals the sum of the forces on the left face and the right face:

\[\begin{split} F_{net} & = p\; dy\; dz - (p + dp)\; dy\; dz \ & = p\; dy\; dz\; - p\; dy\; dz - dp\; dy\; dz \\ & = -dp\; dy\; dz \\ ma & = -dp\; dy\; dz \ldotp \end{split}\]

Figure \(\PageIndex{6}\):

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = \(\rho\)V = \(\rho\) dx dy dz. We have

\[\begin{split} ma & = -dp\; dy\; dz \\ a & = - \frac{dp\; dy\; dz}{m} = - \frac{dp\; dy\; dz}{\rho\; dx\; dy\; dz} = - \frac{dp}{\rho\; dx} \\ \frac{dv}{dt} & = - \frac{dp}{\rho\; dx} \\ dv & = - \frac{dp}{\rho dx} dt = - \frac{dp}{\rho} \frac{1}{v} \\ \rho v\; dv & = -dp \ldotp \end{split}\]

From the continuity equation \(\rho\) dv = −vd\(\rho\), we obtain

\[\begin{split} \rho v\; dv & = -dp \\ (-v\; d \rho)v & = -dp \\ v & = \sqrt{\frac{dp}{d \rho}} \ldotp \end{split}\]

Consider a sound wave moving through air. During the process of compression and expansion of the gas, no heat is added or removed from the system. A process where heat is not added or removed from the system is known as an adiabatic system. Adiabatic processes are covered in detail in The First Law of Thermodynamics , but for now it is sufficient to say that for an adiabatic process, \(pV^{\gamma} = \text{constant}\), where \(p\) is the pressure, \(V\) is the volume, and gamma (\(\gamma\)) is a constant that depends on the gas. For air, \(\gamma\) = 1.40. The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = \(\frac{nM}{\rho}\). The number of moles and the molar mass are constant and can be absorbed into the constant p \(\left(\dfrac{1}{\rho}\right)^{\gamma}\) = constant. Taking the natural logarithm of both sides yields ln p − \(\gamma\) ln \(\rho\) = constant. Differentiating with respect to the density, the equation becomes

\[\begin{split} \ln p - \gamma \ln \rho & = constant \\ \frac{d}{d \rho} (\ln p - \gamma \ln \rho) & = \frac{d}{d \rho} (constant) \\ \frac{1}{p} \frac{dp}{d \rho} - \frac{\gamma}{\rho} & = 0 \\ \frac{dp}{d \rho} & = \frac{\gamma p}{\rho} \ldotp \end{split}\]

If the air can be considered an ideal gas, we can use the ideal gas law:

\[\begin{split} pV & = nRT = \frac{m}{M} RT \\ p & = \frac{m}{V} \frac{RT}{M} = \rho \frac{RT}{M} \ldotp \end{split}\]

Here M is the molar mass of air:

\[\frac{dp}{d \rho} = \frac{\gamma p}{\rho} = \frac{\gamma \left(\rho \frac{RT}{M}\right)}{\rho} = \frac{\gamma RT}{M} \ldotp\]

Since the speed of sound is equal to v = \(\sqrt{\frac{dp}{d \rho}}\), the speed is equal to

\[v = \sqrt{\frac{\gamma RT}{M}} \ldotp\]

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, \(\gamma\) = 1.4, M = 0.02897 kg/mol, and R = 8.31 J/mol • K. If the temperature is T C = 20 °C (T = 293 K), the speed of sound is v = 343 m/s. The equation for the speed of sound in air v = \(\sqrt{\frac{\gamma RT}{M}}\) can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

\[\begin{split} v & = \sqrt{\frac{\gamma RT}{M}} \\ & = \sqrt{\frac{\gamma RT}{M} \left(\dfrac{273\; K}{273\; K}\right)} = \sqrt{\frac{(273\; K) \gamma R}{M}} \sqrt{\frac{T}{273\; K}} \\ & \approx 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \end{split}\]

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

\[v = f \lambda \ldotp\]

In a given medium under fixed conditions, \(v\) is constant, so there is a relationship between \(f\) and \(\lambda\); the higher the frequency, the smaller the wavelength (Figure \(\PageIndex{7}\)).

Example \(\PageIndex{1}\): Calculating Wavelengths

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0 °C air. (Assume that the frequency values are accurate to two significant figures.)

To find wavelength from frequency, we can use \(v = f \lambda\).

• Identify knowns. The value for \(v\) is given by \[v = 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \nonumber\]
• Convert the temperature into kelvins and then enter the temperature into the equation \[v = 331\; m/s \sqrt{\frac{303\; K}{273\; K}} = 348.7\; m/s \ldotp \nonumber\]
• Solve the relationship between speed and wavelength for \(\lambda\): $$\lambda = \frac{v}{f} \ldotp \nonumber$$
• Enter the speed and the minimum frequency to give the maximum wavelength: \[\lambda_{max} = \frac{348.7\; m/s}{20\; Hz} = 17\; m \ldotp \nonumber\]
• Enter the speed and the maximum frequency to give the minimum wavelength: \[\lambda_{min} = \frac{348.7\; m/s}{20,000\; Hz} = 0.017\; m = 1.7\; cm \ldotp \nonumber\]

Significance

Because the product of \(f\) multiplied by \(\lambda\) equals a constant, the smaller \(f\) is, the larger \(\lambda\) must be, and vice versa.

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If \(v\) changes and \(f\) remains the same, then the wavelength \(\lambda\) must change. That is, because \(v = f \lambda\), the higher the speed of a sound, the greater its wavelength for a given frequency.

Exercise \(\PageIndex{1}\)

Imagine you observe two firework shells explode. You hear the explosion of one as soon as you see it. However, you see the other shell for several milliseconds before you hear the explosion. Explain why this is so.

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves, which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced (Figure \(\PageIndex{8}\)).

As sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. The power per unit area is known as the intensity, and in the next section, we will discuss how the intensity depends on the distance from the source.

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by Chris Woodford . Last updated: July 23, 2023.

Photo: Sound is energy we hear made by things that vibrate. Photo by William R. Goodwin courtesy of US Navy and Wikimedia Commons .

What is sound?

Photo: Sensing with sound: Light doesn't travel well through ocean water: over half the light falling on the sea surface is absorbed within the first meter of water; 100m down and only 1 percent of the surface light remains. That's largely why mighty creatures of the deep rely on sound for communication and navigation. Whales, famously, "talk" to one another across entire ocean basins, while dolphins use sound, like bats, for echolocation. Photo by Bill Thompson courtesy of US Fish and Wildlife Service .

Robert Boyle's classic experiment

Artwork: Robert Boyle's famous experiment with an alarm clock.

How sound travels

Artwork: Sound waves and ocean waves compared. Top: Sound waves are longitudinal waves: the air moves back and forth along the same line as the wave travels, making alternate patterns of compressions and rarefactions. Bottom: Ocean waves are transverse waves: the water moves back and forth at right angles to the line in which the wave travels.

The science of sound waves

Picture: Reflected sound is extremely useful for "seeing" underwater where light doesn't really travel—that's the basic idea behind sonar. Here's a side-scan sonar (reflected sound) image of a World War II boat wrecked on the seabed. Photo courtesy of U.S. National Oceanographic and Atmospheric Administration, US Navy, and Wikimedia Commons .

Whispering galleries and amphitheaters

Photos by Carol M. Highsmith: 1) The Capitol in Washington, DC has a whispering gallery inside its dome. Photo credit: The George F. Landegger Collection of District of Columbia Photographs in Carol M. Highsmith's America, Library of Congress , Prints and Photographs Division. 2) It's easy to hear people talking in the curved memorial amphitheater building at Arlington National Cemetery, Arlington, Virginia. Photo credit: Photographs in the Carol M. Highsmith Archive, Library of Congress , Prints and Photographs Division.

Measuring waves

Understanding amplitude and frequency, why instruments sound different, the speed of sound.

Photo: Breaking through the sound barrier creates a sonic boom. The mist you can see, which is called a condensation cloud, isn't necessarily caused by an aircraft flying supersonic: it can occur at lower speeds too. It happens because moist air condenses due to the shock waves created by the plane. You might expect the plane to compress the air as it slices through. But the shock waves it generates alternately expand and contract the air, producing both compressions and rarefactions. The rarefactions cause very low pressure and it's these that make moisture in the air condense, producing the cloud you see here. Photo by John Gay courtesy of US Navy and Wikimedia Commons .

Why does sound go faster in some things than in others?

Chart: Generally, sound travels faster in solids (right) than in liquids (middle) or gases (left)... but there are exceptions!

How to measure the speed of sound

Sound in practice, if you liked this article..., find out more, on this website.

• Electric guitars
• Speech synthesis
• Synthesizers

On other sites

• Explore Sound : A comprehensive educational site from the Acoustical Society of America, with activities for students of all ages.
• Sound Waves : A great collection of interactive science lessons from the University of Salford, which explains what sound waves are and the different ways in which they behave.

Educational books for younger readers

• Sound (Science in a Flash) by Georgia Amson-Bradshaw. Franklin Watts/Hachette, 2020. Simple facts, experiments, and quizzes fill this book; the visually exciting design will appeal to reluctant readers. Also for ages 7–9.
• Sound by Angela Royston. Raintree, 2017. A basic introduction to sound and musical sounds, including simple activities. Ages 7–9.
• Experimenting with Sound Science Projects by Robert Gardner. Enslow Publishers, 2013. A comprehensive 120-page introduction, running through the science of sound in some detail, with plenty of hands-on projects and activities (including welcome coverage of how to run controlled experiments using the scientific method). Ages 9–12.
• Cool Science: Experiments with Sound and Hearing by Chris Woodford. Gareth Stevens Inc, 2010. One of my own books, this is a short introduction to sound through practical activities, for ages 9–12.
• Adventures in Sound with Max Axiom, Super Scientist by Emily Sohn. Capstone, 2007. The original, graphic novel (comic book) format should appeal to reluctant readers. Ages 8–10.

Popular science

• The Sound Book: The Science of the Sonic Wonders of the World by Trevor Cox. W. W. Norton, 2014. An entertaining tour through everyday sound science.

Academic books

• Master Handbook of Acoustics by F. Alton Everest and Ken Pohlmann. McGraw-Hill Education, 2015. A comprehensive reference for undergraduates and sound-design professionals.
• The Science of Sound by Thomas D. Rossing, Paul A. Wheeler, and F. Richard Moore. Pearson, 2013. One of the most popular general undergraduate texts.

Text copyright © Chris Woodford 2009, 2021. All rights reserved. Full copyright notice and terms of use .

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Video transcript

Speed of Sound and Light

Most recent answer: 2/14/2017

(published on 10/22/2007)

Follow-Up #1: light/sound time lag

Follow-up #2: light and sound.

(published on 05/16/2013)

Follow-Up #3: The difference in time taken

The time taken to reach a particular distance (in most general sense) depends on how fast someone is moving. The speed of light is much faster than the speed of sound in air. If you want to compare, the speed of sound in air is ~ 343 m/s and the speed of light is 3x10 10 m/s. In other words, light travels 186 thousand miles in 1 second, while sound takes almost 5 seconds to travel 1 mile.

(published on 02/14/2017)

Follow-up on this answer

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Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is

The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period of time.

Factors Affecting Wave Speed

The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity. (Elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed ( v ) of a wave, thus yielding this general pattern:

Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property . The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. As stated above, sound waves travel faster in solids than they do in liquids than they do in gases. However, within a single phase of matter, the inertial property of density tends to be the property that has a greatest impact upon the speed of sound. A sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium than it will in air. This is mostly due to the lower mass of Helium particles as compared to air particles.  

The Speed of Sound in Air

The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor being present in air. Like any liquid, water has a tendency to evaporate. As it does, particles of gaseous water become mixed in the air. This additional matter will affect the mass density of the air (an inertial property). The temperature will affect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:

where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

v = 331 m/s + (0.6 m/s/C)•(20 C)

v = 331 m/s + 12 m/s

v = 343 m/s

(The above equation relating the speed of a sound wave in air to the temperature provides reasonably accurate speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)

Look It Up!

Using wave speed to determine distances.

At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and the lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of

If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.

Another phenomenon related to the perception of time delays between two events is an echo . A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 1.40 seconds after making the holler , then the distance to the canyon wall can be found as follows:

The canyon wall is 242 meters away. You might have noticed that the time of 0.70 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.

While an echo is of relatively minimal importance to humans, echolocation is an essential trick of the trade for bats. Being a nocturnal creature, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves that reflect off objects in their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses. These bats are utilizing the physics of the Doppler effect discussed in an earlier unit (and also to be discussed later in Lesson 3 ). This method of echolocation enables a bat to navigate and to hunt.

The Wave Equation Revisited

Like any wave, a sound wave has a speed that is mathematically related to the frequency and the wavelength of the wave. As discussed in a previous unit , the mathematical relationship between speed, frequency and wavelength is given by the following equation.

Using the symbols v , λ , and f , the equation can be rewritten as

Check Your Understanding

1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object?

Answer = 25.5 m

The speed of the sound wave is 340 m/s. The distance can be found using d = v • t resulting in an answer of 25.5 m. Use 0.075 seconds for the time since 0.150 seconds refers to the round-trip distance.

2. On a hot summer day, a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second.

a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

Part a Answer: 600 Hz (given)

Part b Answer: 0.583 meters

3. Doubling the frequency of a wave source doubles the speed of the waves.

a. True b. False

Doubling the frequency will halve the wavelength; speed is unaffected by the alteration in the frequency. The speed of a wave depends upon the properties of the medium.

4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C.

 Answer: 1.35 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 256 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

5. Most people can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to this upper range of audible hearing.

Answer: 0.0173 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 20 000 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

6. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.

Answer: 34.5 meters

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 10 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

7. Determine the speed of sound on a cold winter day (T=3 degrees C).

Answer: 332.8 m/s

The speed of sound in air is dependent upon the temperature of air. The dependence is expressed by the equation:

v = 331 m/s + (0.6 m/s/C) • T

where T is the temperature in Celsius. Substitute and solve.

v = 331 m/s + (0.6 m/s/C) • 3 C v = 331 m/s + 1.8 m/s v = 332.8 m/s

8. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls?

Answer = 209 m

The speed of the sound wave at this temperature is 343 m/s (using the equation described in the Tutorial). The distance can be found using d = v • t resulting in an answer of 343 m. Use 0.61 second for the time since 1.22 seconds refers to the round-trip distance.

9. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The velocity of wave B must be __________ the velocity of wave A.

a. one-ninth b. one-third c. the same as d. three times larger than

The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.

10. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.

Since Wave B has three times the wavelength of Wave A, it must have one-third the frequency. Frequency and wavelength are inversely related.

• Interference and Beats

What if the speed of sound were as fast as the speed of light?

Simultaneous thunder and lightning is only the beginning.

The clouds are hanging low on the horizon; the air is sticky and sizzling with electricity. Suddenly, a silent bolt of lightning cracks open the sky. The boom follows a full four seconds later. 

Compared with light , which moves at a stunning 186,000 miles per second (300,000 kilometers per second), sound waves are downright sluggish, moving through air at 0.2 miles per second (0.3 km per second). That's why you see lightning before you hear the thunder. But what would happen if the speed of sound suddenly were a million times faster — the same as the speed of light?

Of course, thunder would reach you at the precise moment of lightning. But that bolt of lightning would also look pretty eerie. Sound waves are composed of particles, each moving slightly enough to collide into the next. That creates areas of higher and lower density within the wave, said George Gollin, a professor of physics at the University of Illinois at Urbana-Champaign. Just think of a slinky: as the toy moves, the coils continually bunch together and then spread out again. Sound waves are similar. At slow speeds, that change in density is imperceptible. At the speed of light, it's a different story. 

Related: What would happen if the speed of light were much lower?

"What would happen is you have pretty humid air [during a lightning storm], the sound wave comes through and squeezes stuff really hard, and then expands out and the pressure drops a lot," Gollin told Live Science. Because pressure corresponds to temperature , the sudden drop in air pressure after a clap of thunder would cause the humid air to freeze. You'd see the lightning bolt through a dense fog of ice crystals. 

An ultra-fast speed of sound would completely change the way our world sounds. Voices would sound particularly strange, Gollin said. When we speak, our vocal cords vibrate to produce sound waves of many different frequencies, pumping them into the larynx, or voice box. There, waves of the same frequency add together to produce much bigger waves — which translates to louder sound. However, not all frequencies add together in the same way. Some sync up perfectly, while others actually interfere with one another, producing a smaller wave and a quieter sound. If the sound moved faster in air, it would change the way waves added together, making certain frequencies louder and others quieter. In sound waves, frequency translates to pitch, so what you get is a very odd sounding voice.

To get a sense of what we'd sound like in a universe where the speed of sound moved ultra-fast, imagine how you sound when you take a deep breath out of a helium balloon — like Mickey Mouse. That's because sound waves move three times faster through helium , said William Robertson, a professor in the department of physics and astronomy at Middle Tennessee State University. "And we're talking about making the speed of sound a million times bigger," Robertson said.

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And if the speed of sound were to suddenly speed up, it would wreak havoc on orchestras, Robertson said. When sound moves back and forth inside the cavity of an oboe or a trumpet, it produces a standing wave. These standing waves behave like those heavy ropes you see tethered to the wall at the gym. When a weight-lifter shakes them fast enough, waves begin oscillating up and down without appearing to travel across the rope. As the ropes are shaken faster and faster, the number of waves — in other words, their frequency — increases. Similarly, when the sound waves produced by wind instruments increase in speed, they increase in frequency. Because higher frequency means higher pitch, wind instruments would produce sounds so high in pitch, they'd be impossible for humans to hear. We would have to design wind instruments to be a million times longer to keep them in tune with the violins and cellos, Robertson said. (A change in the speed of sound as it moves through air wouldn't change the speed of sound along a string, he added.)

— What would it be like to travel faster than the speed of light?

— What if there were no gravity?

— If there were a time warp, how would physicists find it?

Alas, humans wouldn't survive to experience these spectacular changes. Even the soft whistle of a flute would blast anything in its vicinity to smithereens. Light travels in electromagnetic waves, which aren't composed of matter, but sound waves are mechanical — composed of particles colliding into one another. A molecule traveling at the speed of light would have "nearly infinite energy," Gollin said. It would blast through every particle it encountered, sending electrons flying and producing a "spray" of matter and antimatter — particles generated in ultra-high speed collisions that have properties opposite to those of matter. 

"The effects would just be extraordinary," Gollin said. 

Editor's note: Updated at 2:09 p.m. EST Nov. 30 to correct the article's explanation of how vocal cords and the voice box produce sound.

Originally published on Live Science .

Isobel Whitcomb is a contributing writer for Live Science who covers the environment, animals and health. Her work has appeared in the New York Times, Fatherly, Atlas Obscura, Hakai Magazine and Scholastic's Science World Magazine. Isobel's roots are in science. She studied biology at Scripps College in Claremont, California, while working in two different labs and completing a fellowship at Crater Lake National Park. She completed her master's degree in journalism at NYU's Science, Health, and Environmental Reporting Program. She currently lives in Portland, Oregon.

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A Groundbreaking Scientific Discovery Just Gave Humanity the Keys to Interstellar Travel

In a first, this warp drive actually obeys the laws of physics.

If a superluminal—meaning faster than the speed of light—warp drive like Alcubierre’s worked, it would revolutionize humanity’s endeavors across the universe , allowing us, perhaps, to reach Alpha Centauri, our closest star system, in days or weeks even though it’s four light years away.

However, the Alcubierre drive has a glaring problem: the force behind its operation, called “negative energy,” involves exotic particles—hypothetical matter that, as far as we know, doesn’t exist in our universe. Described only in mathematical terms, exotic particles act in unexpected ways, like having negative mass and working in opposition to gravity (in fact, it has “anti-gravity”). For the past 30 years, scientists have been publishing research that chips away at the inherent hurdles to light speed revealed in Alcubierre’s foundational 1994 article published in the peer-reviewed journal Classical and Quantum Gravity .

Now, researchers at the New York City-based think tank Applied Physics believe they’ve found a creative new approach to solving the warp drive’s fundamental roadblock. Along with colleagues from other institutions, the team envisioned a “positive energy” system that doesn’t violate the known laws of physics . It’s a game-changer, say two of the study’s authors: Gianni Martire, CEO of Applied Physics, and Jared Fuchs, Ph.D., a senior scientist there. Their work, also published in Classical and Quantum Gravity in late April, could be the first chapter in the manual for interstellar spaceflight.

POSITIVE ENERGY MAKES all the difference. Imagine you are an astronaut in space, pushing a tennis ball away from you. Instead of moving away, the ball pushes back, to the point that it would “take your hand off” if you applied enough pushing force, Martire tells Popular Mechanics . That’s a sign of negative energy, and, though the Alcubierre drive design requires it, there’s no way to harness it.

Instead, regular old positive energy is more feasible for constructing the “ warp bubble .” As its name suggests, it’s a spherical structure that surrounds and encloses space for a passenger ship using a shell of regular—but incredibly dense—matter. The bubble propels the spaceship using the powerful gravity of the shell, but without causing the passengers to feel any acceleration. “An elevator ride would be more eventful,” Martire says.

That’s because the density of the shell, as well as the pressure it exerts on the interior, is controlled carefully, Fuchs tells Popular Mechanics . Nothing can travel faster than the speed of light, according to the gravity-bound principles of Albert Einstein’s theory of general relativity . So the bubble is designed such that observers within their local spacetime environment—inside the bubble—experience normal movement in time. Simultaneously, the bubble itself compresses the spacetime in front of the ship and expands it behind the ship, ferrying itself and the contained craft incredibly fast. The walls of the bubble generate the necessary momentum, akin to the momentum of balls rolling, Fuchs explains. “It’s the movement of the matter in the walls that actually creates the effect for passengers on the inside.”

Building on its 2021 paper published in Classical and Quantum Gravity —which details the same researchers’ earlier work on physical warp drives—the team was able to model the complexity of the system using its own computational program, Warp Factory. This toolkit for modeling warp drive spacetimes allows researchers to evaluate Einstein’s field equations and compute the energy conditions required for various warp drive geometries. Anyone can download and use it for free . These experiments led to what Fuchs calls a mini model, the first general model of a positive-energy warp drive. Their past work also demonstrated that the amount of energy a warp bubble requires depends on the shape of the bubble; for example, the flatter the bubble in the direction of travel, the less energy it needs.

THIS LATEST ADVANCEMENT suggests fresh possibilities for studying warp travel design, Erik Lentz, Ph.D., tells Popular Mechanics . In his current position as a staff physicist at Pacific Northwest National Laboratory in Richland, Washington, Lentz contributes to research on dark matter detection and quantum information science research. His independent research in warp drive theory also aims to be grounded in conventional physics while reimagining the shape of warped space. The topic needs to overcome many practical hurdles, he says.

Controlling warp bubbles requires a great deal of coordination because they involve enormous amounts of matter and energy to keep the passengers safe and with a similar passage of time as the destination. “We could just as well engineer spacetime where time passes much differently inside [the passenger compartment] than outside. We could miss our appointment at Proxima Centauri if we aren’t careful,” Lentz says. “That is still a risk if we are traveling less than the speed of light.” Communication between people inside the bubble and outside could also become distorted as it passes through the curvature of warped space, he adds.

While Applied Physics’ current solution requires a warp drive that travels below the speed of light, the model still needs to plug in a mass equivalent to about two Jupiters. Otherwise, it will never achieve the gravitational force and momentum high enough to cause a meaningful warp effect. But no one knows what the source of this mass could be—not yet, at least. Some research suggests that if we could somehow harness dark matter , we could use it for light-speed travel, but Fuchs and Martire are doubtful, since it’s currently a big mystery (and an exotic particle).

Despite the many problems scientists still need to solve to build a working warp drive, the Applied Physics team claims its model should eventually get closer to light speed. And even if a feasible model remains below the speed of light, it’s a vast improvement over today’s technology. For example, traveling at even half the speed of light to Alpha Centauri would take nine years. In stark contrast, our fastest spacecraft, Voyager 1—currently traveling at 38,000 miles per hour—would take 75,000 years to reach our closest neighboring star system.

Of course, as you approach the actual speed of light, things get truly weird, according to the principles of Einstein’s special relativity . The mass of an object moving faster and faster would increase infinitely, eventually requiring an infinite amount of energy to maintain its speed.

“That’s the chief limitation and key challenge we have to overcome—how can we have all this matter in our [bubble], but not at such a scale that we can never even put it together?” Martire says. It’s possible the answer lies in condensed matter physics, he adds. This branch of physics deals particularly with the forces between atoms and electrons in matter. It has already proven fundamental to several of our current technologies, such as transistors, solid-state lasers, and magnetic storage media.

The other big issue is that current models allow a stable warp bubble, but only for a constant velocity. Scientists still need to figure out how to design an initial acceleration. On the other end of the journey, how will the ship slow down and stop? “It’s like trying to grasp the automobile for the first time,” Martire says. “We don’t have an engine just yet, but we see the light at the end of the tunnel.” Warp drive technology is at the stage of 1882 car technology, he says: when automobile travel was possible, but it still looked like a hard, hard problem.

The Applied Physics team believes future innovations in warp travel are inevitable. The general positive energy model is a first step. Besides, you don’t need to zoom at light speed to achieve distances that today are just a dream, Martire says. “Humanity is officially, mathematically, on an interstellar track.”

Before joining Popular Mechanics , Manasee Wagh worked as a newspaper reporter, a science journalist, a tech writer, and a computer engineer. She’s always looking for ways to combine the three greatest joys in her life: science, travel, and food.

.css-cuqpxl:before{padding-right:0.3125rem;content:'//';display:inline;} Physics .css-xtujxj:before{padding-left:0.3125rem;content:'//';display:inline;}

The Source of All Consciousness May Be Black Holes

Immortality Is Impossible Until We Beat Physics

How a Lunar Supercollider Could Upend Physics

Is Consciousness Everywhere All at Once?

One Particle Could Shatter Our Concept of Reality

Do Black Holes Die?

Are Multiverse Films Like ‘The Flash’ Realistic?

Why Time Reflections Are a ‘Holy Grail’ in Physics

Why Our Existence Always Contains Some Uncertainty

Copies of You Could Live Inside Quantum Computers

There’s an ‘Anti-Universe’ Going Backward in Time

Is the Speed of Light Slowing Down?

Philip perry | big think.

Modern physics rests on the foundational notion that the speed of light is a constant, which in a vacuum is 186,000 miles per second (299,792 km/s). Einstein established this within his theory of general relativity, first developed in 1906 when he was just 26 years-old. But what if it doesn’t? A few albeit controversial incidents in recent years challenge the idea that light always travels at a constant speed. And in fact, we’ve known for a long time that there are several phenomena that travel faster than light, without violating the theory of relativity.

For instance, whereas traveling faster than sound creates a sonic boom, traveling faster than light creates a “luminal boom.” Russian scientist Pavel Alekseyevich Cherenkov discovered this in 1934, which won him the Nobel Prize in Physics in 1958. Cherenkov radiation can be observed in the core of a nuclear reactor. When the core is submerged in water to cool it, electrons move through the water faster than the speed of light, causing a luminal boom.

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New Russian weapon can travel 27 times the speed of sound

MOSCOW (AP) — A new intercontinental weapon that can fly 27 times the speed of sound became operational Friday, Russia’s defense minister reported to President Vladimir Putin, bolstering the country’s nuclear strike capability.

Putin has described the Avangard hypersonic glide vehicle as a technological breakthrough comparable to the 1957 Soviet launch of the first satellite. The new Russian weapon and a similar system being developed by China have troubled the United States, which has pondered defense strategies.

The Avangard is launched atop an intercontinental ballistic missile, but unlike a regular missile warhead that follows a predictable path after separation it can make sharp maneuvers in the atmosphere en route to target, making it much harder to intercept.

Defense Minister Sergei Shoigu informed Putin that the first missile unit equipped with the Avangard hypersonic glide vehicle entered combat duty.

“I congratulate you on this landmark event for the military and the entire nation,” Shoigu said later during a conference call with top military leaders.

The Strategic Missile Forces chief, Gen. Sergei Karakayev, said during the call that the Avangard was put on duty with a unit in the Orenburg region in the southern Ural Mountains.

Putin unveiled the Avangard among other prospective weapons systems in his state-of-the-nation address in March 2018, noting that its ability to make sharp maneuvers on its way to a target will render missile defense useless.

“It heads to target like a meteorite, like a fireball,” he said at the time.

The Russian leader noted that Avangard is designed using new composite materials to withstand temperatures of up to 2,000 Celsius (3,632 Fahrenheit) resulting from a flight through the atmosphere at hypersonic speeds.

The military said the Avangard is capable of flying 27 times faster than the speed of sound. It carries a nuclear weapon of up to 2 megatons.

Putin has said Russia had to develop the Avangard and other prospective weapons systems because of U.S. efforts to develop a missile defense system that he claimed could erode Russia’s nuclear deterrent. Moscow has scoffed at U.S. claims that its missile shield isn’t intended to counter Russia’s massive missile arsenals.

Earlier this week, Putin emphasized that Russia is the only country armed with hypersonic weapons. He noted that for the first time Russia is leading the world in developing an entire new class of weapons, unlike in the past when it was catching up with the U.S.

In December 2018, the Avangard was launched from the Dombarovskiy missile base in the southern Urals and successfully hit a practice target on the Kura shooting range on Kamchatka, 6,000 kilometers (3,700 miles) away.

Russian media reports indicated that the Avangard will first be mounted on Soviet-built RS-18B intercontinental ballistic missiles, code-named SS-19 by NATO. It is expected to be fitted to the prospective Sarmat heavy intercontinental ballistic missile after it becomes operational.

The Defense Ministry said last month it demonstrated the Avangard to a team of U.S. inspectors as part of transparency measures under the New Start nuclear arms treaty with the U.S.

The Russian military previously had commissioned another hypersonic weapon of a smaller range.

The Kinzhal (Dagger), which is carried by MiG-31 fighter jets, entered service with the Russian air force last year. Putin has said the missile flies 10 times faster than the speed of sound, has a range of more than 2,000 kilometers (1,250 miles) and can carry a nuclear or a conventional warhead. The military said it is capable of hitting both land targets and navy ships.

China has tested its own hypersonic glide vehicle, believed to be capable of traveling at least five times the speed of sound. It displayed the weapon called Dong Feng 17, or DF-17, at a military parade marking the 70th anniversary of the founding of the Chinese state.

U.S. officials have talked about putting a layer of sensors in space to more quickly detect enemy missiles, particularly the hypersonic weapons. The administration also plans to study the idea of basing interceptors in space, so the U.S. can strike incoming enemy missiles during the first minutes of flight when the booster engines are still burning.

The Pentagon also has been working on the development of hypersonic weapons in recent years, and Defense Secretary Mark Esper said in August that he believes “it’s probably a matter of a couple of years” before the U.S. has one. He has called it a priority as the military works to develop new long-range fire capabilities.

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New Russian weapon can travel 27 times the speed of sound

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MOSCOW (AP) — A new intercontinental weapon that can fly 27 times the speed of sound became operational Friday, Russia’s defense minister reported to President Vladimir Putin, bolstering the country’s nuclear strike capability.

Putin has described the Avangard hypersonic glide vehicle as a technological breakthrough comparable to the 1957 Soviet launch of the first satellite. The new Russian weapon and a similar system being developed by China have troubled the United States, which has pondered defense strategies.

The Avangard is launched atop an intercontinental ballistic missile, but unlike a regular missile warhead that follows a predictable path after separation it can make sharp maneuvers in the atmosphere en route to target, making it much harder to intercept.

Defense Minister Sergei Shoigu informed Putin that the first missile unit equipped with the Avangard hypersonic glide vehicle entered combat duty.

“I congratulate you on this landmark event for the military and the entire nation,” Shoigu said later during a conference call with top military leaders.

The Strategic Missile Forces chief, Gen. Sergei Karakayev, said during the call that the Avangard was put on duty with a unit in the Orenburg region in the southern Ural Mountains.

Putin unveiled the Avangard among other prospective weapons systems in his state-of-the-nation address in March 2018, noting that its ability to make sharp maneuvers on its way to a target will render missile defense useless.

“It heads to target like a meteorite, like a fireball,” he said at the time.

The Russian leader noted that Avangard is designed using new composite materials to withstand temperatures of up to 2,000 Celsius (3,632 Fahrenheit) resulting from a flight through the atmosphere at hypersonic speeds.

The military said the Avangard is capable of flying 27 times faster than the speed of sound. It carries a nuclear weapon of up to 2 megatons.

Putin has said Russia had to develop the Avangard and other prospective weapons systems because of U.S. efforts to develop a missile defense system that he claimed could erode Russia’s nuclear deterrent. Moscow has scoffed at U.S. claims that its missile shield isn’t intended to counter Russia’s massive missile arsenals.

Earlier this week, Putin emphasized that Russia is the only country armed with hypersonic weapons. He noted that for the first time Russia is leading the world in developing an entire new class of weapons, unlike in the past when it was catching up with the U.S.

In December 2018, the Avangard was launched from the Dombarovskiy missile base in the southern Urals and successfully hit a practice target on the Kura shooting range on Kamchatka, 6,000 kilometers (3,700 miles) away.

Russian media reports indicated that the Avangard will first be mounted on Soviet-built RS-18B intercontinental ballistic missiles, code-named SS-19 by NATO. It is expected to be fitted to the prospective Sarmat heavy intercontinental ballistic missile after it becomes operational.

The Defense Ministry said last month it demonstrated the Avangard to a team of U.S. inspectors as part of transparency measures under the New Start nuclear arms treaty with the U.S.

The Russian military previously had commissioned another hypersonic weapon of a smaller range.

The Kinzhal (Dagger), which is carried by MiG-31 fighter jets, entered service with the Russian air force last year. Putin has said the missile flies 10 times faster than the speed of sound, has a range of more than 2,000 kilometers (1,250 miles) and can carry a nuclear or a conventional warhead. The military said it is capable of hitting both land targets and navy ships.

China has tested its own hypersonic glide vehicle, believed to be capable of traveling at least five times the speed of sound. It displayed the weapon called Dong Feng 17, or DF-17, at a military parade marking the 70th anniversary of the founding of the Chinese state.

U.S. officials have talked about putting a layer of sensors in space to more quickly detect enemy missiles, particularly the hypersonic weapons. The administration also plans to study the idea of basing interceptors in space, so the U.S. can strike incoming enemy missiles during the first minutes of flight when the booster engines are still burning.

The Pentagon also has been working on the development of hypersonic weapons in recent years, and Defense Secretary Mark Esper said in August that he believes “it’s probably a matter of a couple of years” before the U.S. has one. He has called it a priority as the military works to develop new long-range fire capabilities.

Ukraine-Russia war latest: Kyiv launches major attack on Crimea naval base using Western weapons

The early-morning attack in Crimea was carried out with weapons from Kyiv's allies - which were "extremely effective", a Ukrainian military source said. Meanwhile, the Russian foreign minister has said he hopes nuclear drills will "knock sense" into the West after jets were pledged.

Thursday 30 May 2024 20:02, UK

• Ukraine launches major attack against Russian base in Crimea  
• Moscow hopes nuclear drills will 'knock sense' into West over fighter jet plans
• Italy says no to Ukraine using Western weapons to strike Russia
• Putin names ex-bodyguard for senior role - fuelling succession rumours
• Siobhan Robbins eyewitness:  NATO's biggest drill since the Cold War is a warning for Putin to stay away
• The big picture : What you need to know about the war right now

NATO operation Steadfast Defender continues across Europe - the largest exercises since the Cold War. 

The exercise is widely interpreted as preparation or a simulation of a response to a potential conflict with Russia.

Sky's Europe correspondent Siobhan Robbins watched as tanks, helicopters and soldiers took part. 

The US is close to completing a deal that would secure the bilateral security agreement with Ukraine that Joe Biden announced last year at a G7 meeting, a source has told Reuters. 

G7 nations, led by Washington, unveiled a framework in July for the long-term security of Ukraine to boost its defences against Russia.

The comments from the official come after a Financial Times report published earlier today which claimed a deal was close. 

Fierce fighting is intensifying near the eastern city of Pokrovsk, Ukraine's general staff has reported.

"The number of engagements in the Pokrovsk sector remains the highest," it said in its afternoon update. 

The area, just northwest of the city of Donetsk, has had an increase in Russian activity in recent weeks. 

"The enemy has already made 18 offensive attempts there [today]," it reported. 

Five combat engagements have started in the vicinity of Novooleksandrivka, it added, noting a village about 30km east of Pokrovsk.

"Our troops also continue to repel the aggressor," the general staff said. 

Building our last post - NATO chief Jens Stoltenberg is set to ask allies to pledge some €40bn in military aid to Ukraine each year, a source inside the alliance has told the Reuters news agency. 

The funding would sustain at least the current levels of military support allies have been sending. 

"We need to sustain that current level of support as a minimum to provide the predictability Ukraine needs, for as long as necessary," the NATO source said, adding that allies had provided some €40bn per year since Russia's full-scale invasion of Ukraine in 2022. 

No such deal has been publicly announced as of yet, but foreign minsters from allies are in Prague for talks currently. 

NATO's secretary general Jens Stoltenberg says Ukraine can win its war against Russia, but only if allies give "continued robust support".

Speaking ahead of a meeting with foreign ministers in Prague, Mr Stoltenberg adds "the time has come" for NATO countries to "consider some of the restrictions on weapons" sent to Ukraine.

The secretary general has also called for the West to lift restrictions on Western weapons being used against targets in Russia throughout the week.

Last month, he suggested allies should commit to providing Kyiv €100bn (£85bn) over the next five years.

France and Germany said yesterday they support Ukraine striking military targets inside Russia, but Italy's foreign minister ruled it out earlier today (see 8.50am post).

Some Western allies have refused to let Ukraine use munitions it has supplied in Russian territory over fears it would escalate the conflict.

Lord Cameron said at the start of the month that  Kyiv could use British weapons  against targets in Russia - which the Kremlin called a "direct escalation".

This morning, Russia said it hopes nuclear deterrence would "knock some sense" into the West after Belgium promised to send 30 F-16 fighter jets to Kyiv over the next four years (see 7am post).

Robert Woodland, a US citizen who was arrested on suspicion of drug trafficking in Russia, has appeared in a Moscow courtroom today.

Standing behind glass nearly five months after his arrest and with a shaved head, Mr Woodland was in court for a hearing.

Mr Woodland was detained in January, though it is unclear why he was in Russia at the time.

Russian media reports at the start of the year said his name matched that of a man who was interviewed by the daily newspaper Komsomolskaya Pravda in 2020.

The man said in the interview that he was born in the Perm region in the Ural Mountains in 1991, and came to Russia to find his mother.

Russia has accused the US, NATO and others of escalating tensions with Ukraine and stoking a "senseless war".

Kremlin spokesman Dmitry Peskov said today the West has "in recent days and weeks embarked on a new round of escalation".

He added: "They are doing this deliberately. We hear a lot of bellicose statements… They are encouraging Ukraine in every possible way to continue this senseless war.

"This will all, of course, inevitably have consequences and will ultimately be very damaging to the interests of those countries that have taken the path of escalation."

Meanwhile, foreign ministers from NATO countries are set to meet in Prague today amid pressure to allow Ukraine to strike targets inside of Russia (see 12.10pm post). 

Since Russia invaded Ukraine on 24 February 2022, NATO countries have since provided military aid worth millions to Kyiv but with strict conditions on its use.

Volodymyr Zelenskyy said yesterday it is "unfair" that Ukraine cannot strike inside Russia despite receiving long-range missiles from the West.

Russian missiles have struck the village of Mala Danylivka today, leaving many buildings in ruins.

The town, just on the outskirts of Kharkiv, was hit as part of Russia's northeastern offensive, which it launched this month.

Foreign ministers from NATO countries are set to meet in Prague later today - as calls to let Ukraine use supplied weapons in Russian territory grow.

Officials will meet for two days ahead of a NATO summit in July, where a new support package for Ukraine is expected to be announced.

Kyiv has been pressing Western supporters, particularly the US, to let it use long-range missiles to hit targets inside of Russia.

France and Germany said yesterday they support Ukraine striking military targets inside Russia, but Italy's foreign minister ruled it out.

In an interview earlier today, Antonio Tajani said "all the weapons leaving from Italy should be used within Ukraine" (see 8.50am post).

Ukraine launched a major attack against a Russian naval base in occupied Crimea early this morning.

At 1am today, the Ukrainian armed forces struck targets near the Kerch Bridge with precision guided missiles.

A Russian Mangust patrol boat was destroyed in the attack, a Ukrainian military source has told Sky News.

The source also confirmed that Western supplied weapons were used, adding they "proved extremely effective against this Russian military target despite high concentrations of Russian Air Defence Systems".

Nikolai Lukashenko, Crimea's Russian-installed transportation chief, claimed on Telegram that Ukraine's overnight attack damaged two transport ferries.

The Kerch Bridge, linking Russia and Crimea over the Kerch Strait, is regularly used by Moscow as a logistics hub to resupply its forces. It was built in 2018 after Russia's illegal annexation of Crimea four years earlier.

Ukraine has launched frequent attacks on the crossing since the war began: in July last year, Kyiv attacked it with two suicide sea drones, damaging a span of the road bridge. 

The explosions  killed two civilians and injured one . Ukraine later formally admitted to launching the attack.

Our military analyst Sean Bell answered a reader's question on why Ukraine can't destroy the bridge earlier this month - click here to read more .

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La Jolla traffic board wants San Diego to adopt practices allowing lower speed limits

A state law gives cities the authority to reduce speed limits on certain roads, particularly those deemed unsafe for pedestrians and cyclists.

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An initiative that could lead to lower speed limits in parts of San Diego has unanimous support from the La Jolla Traffic & Transportation Board.

At its meeting May 21, the board considered a request to advise the city to adopt actions laid out in state Assembly Bill 43 , which gives municipalities the authority to reduce speed limits on roads contiguous to a business district and others that are deemed particularly unsafe for pedestrians and cyclists. They already were authorized to lower the speed limit in school zones.

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The request was presented by Anar Salayev, executive director of BikeSD , a nonprofit that promotes bicycling and cycling infrastructure and safety measures. Salayev said reduced speed limits would be the first step in achieving traffic calming as well as improving road safety.

Supporters of AB 43 cite National Highway Traffic Safety Administration data that says if a person is struck by a vehicle traveling 20 mph, the person has up to a 95 percent chance of surviving, vs. a 20 percent chance if the vehicle is traveling 40 mph.

“On the surface, [the speed] doesn’t seem like that much of a difference, but it’s actually exponential in the potential consequences and outcomes,” Salayev said. “Slower vehicle speeds make for a more comfortable and safer experience, not only for pedestrians but also for cyclists, for anyone in a wheelchair, for really anyone else on that road.”

AB 43 was signed into law in fall 2021, and since then, several California cities have taken a cue from the bill to reduce speed limits across hundreds of miles of roadway. Salayev said San Diego is “ripe” to follow suit, citing a memo in November 2022 from Councilman Stephen Whitburn calling for the city Transportation Department to use AB 43 to develop a list of streets recommended for speed limit reduction.

The memo asked that priority be given to “streets with a history of fatal and severe injury collisions” and that the department “conduct an outreach effort to hear directly from community members regarding suggestions for speed limit reductions.”

A city news release in February 2023 announced that San Diego — aided by a $680,000 grant from the U.S. Department of Transportation — would develop a speed management plan identifying areas where lower speeds would most benefit pedestrians and cyclists.

“Cities have been adopting this,” Salayev said at the T&T Board meeting, “and it’s about time that San Diego does, too.”

“The council members want a list of five corridors from every district where they can start rolling this out immediately,” Salayev said. “You all live and work and commute in La Jolla. You are the right people to let ... the council know where you think speeds could be reduced.”

La Jolla is represented by District 1 Councilman Joe LaCava.

Salayev also suggested that the La Jolla Community Planning Association write a letter to the mayor’s office outlining specific streets the group feels would best be served by lowered speed limits.

When asked about the effectiveness and fiscal impact of the implementation of AB 43 in other cities, Salayev acknowledged that the programs are relatively new and that not enough substantial data has been produced to make firm conclusions.

Some Traffic & Transportation Board members said any speed limit changes need to be accompanied by active enforcement.

“If it’s not going to get enforced, or if there is no mechanism to enforce it … it’s just not going to change the behavior of people who don’t care anyway,” member John Bauer said.

Board Chairman Brian Earley said there is a relative lack of police presence in La Jolla compared with the speeding violations that happen regularly.

“We’re missing enforcement,” Earley said. “We’d really like to see enforcement of surface street speeds, and I don’t know why they can’t park the car, pull out a radar gun and pull people over. We all know the Police Department needs funding. They could increase their revenue and solve a lot of their financial issues in a week.”

California has based speed limits on a process known as the 85th percentile, in which speed surveys conducted by local governments on busy streets every 10 years or so measure the speed at which drivers were traveling, and speed limits are set to reflect what 85 percent of motorists were driving at on a given section of road.

However, in many cases when the 85th-percentile method called for raising speed limits, local officials in San Diego declined to update the limits because of neighborhood opposition and concerns about pedestrian injuries and deaths.

That made the existing speed limit unenforceable, meaning the city had to give up issuing tickets using radar or other electronic devices.

In 2019, The San Diego Union-Tribune , citing data obtained through a public records request, reported that of the 656 streets where the city was responsible for setting speeds, 103 had stretches where police were not allowed to enforce the speed limit by radar — totaling more than 110 miles of roadway.

Streets in La Jolla where that applied included parts of Calle de Oro, La Jolla Parkway, La Jolla Boulevard, Nautilus Street and Via Capri.

San Diego police Officer Jason Costanza said at the time that “complaints about traffic safety are one of the forefront complaints. When we don’t have the ability to enforce the speed, it’s difficult to explain the situation to the public. That’s frustrating for us and the community.”

AB 43 modifies the 85th-percentile method so that motorists’ driving behavior doesn’t need to be the dominant factor in establishing speed limit recommendations.

Board member Tom Hardy brought up automated cameras as a way to get motorists to obey speed limits.

“The streets aren’t safe,” Hardy said. “When pedestrians and cyclists go out in this neighborhood, they’re taking their lives into their own hands.”

Salayev said enforcement likely would come after the establishment of corridors in need of traffic calming.

“This would be a first step to help identify those corridors and roll out this program while working on creative long-term changes down the line that would actually reduce speeds in a significant way,” Salayev said. “What we want to see from there is self-enforcing streets. That could be anything from cameras to ... other sorts of infrastructure later down the line.”

Salayev pointed to Assembly Bill 645 , a law signed by the governor in October that established a speed camera pilot program in six California cities.

Resident Michael McCormack expressed a desire for reduced speed limits in La Jolla Shores.

“This is just like cigarettes in bars in 2000,” McCormack said. “Everyone used to say ‘That’s just the way it is.’ Well, we’re the same way with speed as a community. The speeds are too fast.”

Board member Bill Podway asked about the cost of implementing lower speed limits, adding that the city of San Diego is “dead broke.”

Salayev said the cost of changing speed limit signs would be minimal and could be bundled with another project.

Following the discussion, the board voted to support use of AB 43 by the city. The decision is expected to be reviewed by the Community Planning Association at its meeting in June.

Meanwhile, the San Diego Association of Governments, the county’s regional planning agency, is working to pinpoint high-risk areas for cyclists and pedestrians in its first regionwide “Vision Zero” action plan .

Vision Zero is a road safety concept adopted by 90 U.S. cities, including San Diego, that aims to reduce traffic deaths to zero, even if it slows traffic.

SANDAG is creating two maps as part of its plan. One shows where crashes typically have happened in the past, while the other tries to guess where they will happen in the future.

The first map indicates that 6.1 percent of non-freeway local roadways account for more than half of fatal crashes involving pedestrians and cyclists.

The second map shows locations with the most risk factors that typically predict crashes — such as number of lanes and proximity to apartment complexes or commercial districts.

Sam Sanford, a SANDAG senior regional planner, said the agency also is gathering public input, including through an online survey where nearly 3,000 people singled out potentially dangerous intersections.

He said that could help cities discover problem areas that local officials aren’t aware of.

Other T&T news

Concerts by the Sea: The board also voted unanimously to support the closure of six parking spaces along Coast Boulevard at Scripps Park during the Kiwanis Club of La Jolla’s Concerts by the Sea series this summer.

The spaces will be reserved for musicians to unload and load their equipment.

Four free Sunday concerts are slated for the series, all from 3:30 to 5:30 p.m. at Scripps Park.

The schedule:

• July 14: Atomic Groove (variety dance band)

• July 21: Jimmy Buffett cover band

• July 28: Betamaxx (‘80s music)

• Aug. 4: Big Time Operator (big band music)

Next meeting: The La Jolla Traffic & Transportation Board next meets (pending items to review) at 4 p.m. Tuesday, June 18, at the La Jolla/Riford Library, 7555 Draper Ave.

— San Diego Union-Tribune staff writer David Garrick contributed to this report. ◆

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