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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.

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Speed of Sound in Physics

In physics, the speed of sound is the distance traveled per unit of time by a sound wave through a medium. It is highest for stiff solids and lowest for gases. There is no sound or speed of sound in a vacuum because sound (unlike light ) requires a medium in order to propogate.

What Is the Speed of Sound?

Usually, conversations about the speed of sound refer to the speed of sound of dry air (humidity changes the value). The value depends on temperature.

at 20 ° C or 68 ° F: 343 m/s or 1234.8 kph or 1125ft/s or 767 mph
at 0 ° C or 32 ° F: 331 m/s or 1191.6 kph or 1086 ft/s or 740 mph

Mach Numher

The Mach number is the ratio of air speed to the speed of sound. So, an object at Mach 1 is traveling at the speed of sound. Exceeding Mach 1 is breaking the sound barrier or is supersonic . At Mach 2, the object travels twice the speed of sound. Mach 3 is three times the speed of sound, and so on.

Remember that the speed of sound depends on temperature, so you break sound barrier at a lower speed when the temperature is colder. To put it another way, it gets colder as you get higher in the atmosphere, so an aircraft might break the sound barrier at a higher altitude even if it does not increase its speed.

Solids, Liquids, and Gases

The speed of sound is greatest for solids, intermediate for liquids, and lowest for gases:

v solid > v liquid >v gas

Particles in a gas undergo elastic collisions and the particles are widely separated. In contrast, particles in a solid are locked into place (rigid or stiff), so a vibration readily transmits through chemical bonds.

Here are examples of the difference between the speed of sound in different materials:

Diamond (solid): 12000 m/s
Copper (solid): 6420 m/s
Iron (solid): 5120 m/s
Water (liquid) 1481 m/s
Helium (gas): 965 m/s
Dry air (gas): 343 m/s

Sounds waves transfer energy to matter via a compression wave (in all phases) and also shear wave (in solids). The pressure disturbs a particle, which then impacts its neighbor, and continues traveling through the medium. The speed is how quickly the wave moves, while the frequency is the number of vibrations the particle makes per unit of time.

The Hot Chocolate Effect

The hot chocolate effect describes the phenomenon where the pitch you hear from tapping a cup of hot liquid rises after adding a soluble powder (like cocoa powder into hot water). Stirring in the powder introduces gas bubbles that reduce the speed of sound of the liquid and lower the frequency (pitch) of the waves. Once the bubbles clear, the speed of sound and the frequency increase again.

Speed of Sound Formulas

There are several formulas for calculating the speed of sound. Here are a few of the most common ones:

For gases these approximations work in most situations:

For this formula, use the Celsius temperature of the gas.

v = 331 m/s + (0.6 m/s/C)•T

Here is another common formula:

v = (γRT) 1/2

γ is the ratio of specific heat values or adiabatic index (1.4 for air at STP )
R is a gas constant (282 m 2 /s 2 /K for air)
T is the absolute temperature (Kelvin)

The Newton-Laplace formula works for both gases and liquids (fluids):

v = (K s /ρ) 1/2

K s is the coefficient of stiffness or bulk modulus of elasticity for gases
ρ is the density of the material

So solids, the situation is more complicated because shear waves play into the formula. There can be sound waves with different velocities, depending on the mode of deformation. The simplest formula is for one-dimensional solids, like a long rod of a material:

v = (E/ρ) 1/2

E is Young’s modulus

Note that the speed of sound decreases with density! It increases according to the stiffness of a medium. This is not intuitively obvious, since often a dense material is also stiff. But, consider that the speed of sound in a diamond is much faster than the speed in iron. Diamond is less dense than iron and also stiffer.

Factors That Affect the Speed of Sound

The primary factors affecting the speed of sound of a fluid (gas or liquid) are its temperature and its chemical composition. There is a weak dependence on frequency and atmospheric pressure that is omitted from the simplest equations.

While sound travels only as compression waves in a fluid, it also travels as shear waves in a solid. So, a solid’s stiffness, density, and compressibility also factor into the speed of sound.

Speed of Sound on Mars

Thanks to the Perseverance rover, scientists know the speed of sound on Mars. The Martian atmosphere is much colder than Earth’s, its thin atmosphere has a much lower pressure, and it consists mainly of carbon dioxide rather than nitrogen. As expected, the speed of sound on Mars is slower than on Earth. It travels at around 240 m/s or about 30% slower than on Earth.

What scientists did not expect is that the speed of sound varies for different frequencies. A high pitched sound, like from the rover’s laser, travels faster at around 250 m/s. So, for example, if you listened to a symphony recording from a distance on Mars you’d hear the various instruments at different times. The explanation has to do with the vibrational modes of carbon dioxide, the primary component of the Martian atmosphere. Also, it’s worth noting that the atmospheric pressure is so low that there really isn’t any much sound at all from a source more than a few meters away.

Speed of Sound Example Problems

Find the speed of sound on a cold day when the temperature is 2 ° C.

The simplest formula for finding the answer is the approximation:

v = 331 m/s + (0.6 m/s/C) • T

Since the given temperature is already in Celsius, just plug in the value:

v = 331 m/s + (0.6 m/s/C) • 2 C = 331 m/s + 1.2 m/s = 332.2 m/s

You’re hiking in a canyon, yell “hello”, and hear an echo after 1.22 seconds. The air temperature is 20 ° C. How far away is the canyon wall?

The first step is finding the speed of sound at the temperature:

v = 331 m/s + (0.6 m/s/C) • T v = 331 m/s + (0.6 m/s/C) • 20 C = 343 m/s (which you might have memorized as the usual speed of sound)

Next, find the distance using the formula:

d = v• T d = 343 m/s • 1.22 s = 418.46 m

But, this is the round-trip distance! The distance to the canyon wall is half of this or 209 meters.

If you double the frequency of sound, it double the speed of its waves. True or false?

This is (mostly) false. Doubling the frequency halves the wavelength, but the speed depends on the properties of the medium and not its frequency or wavelength. Frequency only affects the speed of sound for certain media (like the carbon dioxide atmosphere of Mars).

Everest, F. (2001). The Master Handbook of Acoustics . New York: McGraw-Hill. ISBN 978-0-07-136097-5.
Kinsler, L.E.; Frey, A.R.; Coppens, A.B.; Sanders, J.V. (2000). Fundamentals of Acoustics (4th ed.). New York: John Wiley & Sons. ISBN 0-471-84789-5.
Maurice, S.; et al. (2022). “In situ recording of Mars soundscape:. Nature. 605: 653-658. doi: 10.1038/s41586-022-04679-0
Wong, George S. K.; Zhu, Shi-ming (1995). “Speed of sound in seawater as a function of salinity, temperature, and pressure”. The Journal of the Acoustical Society of America . 97 (3): 1732. doi: 10.1121/1.413048

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Video transcript

17.1 Sound Waves

Learning objectives.

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

Explain the difference between sound and hearing
Describe sound as a wave
List the equations used to model sound waves
Describe compression and rarefactions as they relate to sound

The physical phenomenon of sound is a disturbance of matter that is transmitted from its source outward. Hearing is the perception of sound, just as seeing is the perception of visible light. On the atomic scale, sound is a disturbance of atoms that is far more ordered than their thermal motions. In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. Thus, sound waves can induce oscillations and resonance effects ( Figure 17.2 ).

Interactive

This video shows waves on the surface of a wine glass, being driven by sound waves from a speaker. As the frequency of the sound wave approaches the resonant frequency of the wine glass, the amplitude and frequency of the waves on the wine glass increase. When the resonant frequency is reached, the glass shatters.

A speaker produces a sound wave by oscillating a cone, causing vibrations of air molecules. In Figure 17.3 , a speaker vibrates at a constant frequency and amplitude, producing vibrations in the surrounding air molecules. As the speaker oscillates back and forth, it transfers energy to the air, mostly as thermal energy. But a small part of the speaker’s energy goes into compressing and expanding the surrounding air, creating slightly higher and lower local pressures. These compressions (high-pressure regions) and rarefactions (low-pressure regions) move out as longitudinal pressure waves having the same frequency as the speaker—they are the disturbance that is a sound wave. (Sound waves in air and most fluids are longitudinal, because fluids have almost no shear strength. In solids, sound waves can be both transverse and longitudinal.)

Figure 17.3 (a) shows the compressions and rarefactions, and also shows a graph of gauge pressure versus distance from a speaker. As the speaker moves in the positive x -direction, it pushes air molecules, displacing them from their equilibrium positions. As the speaker moves in the negative x -direction, the air molecules move back toward their equilibrium positions due to a restoring force. The air molecules oscillate in simple harmonic motion about their equilibrium positions, as shown in part (b). Note that sound waves in air are longitudinal, and in the figure, the wave propagates in the positive x -direction and the molecules oscillate parallel to the direction in which the wave propagates.

Models Describing Sound

Sound can be modeled as a pressure wave by considering the change in pressure from average pressure,

This equation is similar to the periodic wave equations seen in Waves , where Δ P Δ P is the change in pressure, Δ P max Δ P max is the maximum change in pressure, k = 2 π λ k = 2 π λ is the wave number, ω = 2 π T = 2 π f ω = 2 π T = 2 π f is the angular frequency, and ϕ ϕ is the initial phase. The wave speed can be determined from v = ω k = λ T . v = ω k = λ T . Sound waves can also be modeled in terms of the displacement of the air molecules. The displacement of the air molecules can be modeled using a cosine function:

In this equation, s is the displacement and s max s max is the maximum displacement.

Not shown in the figure is the amplitude of a sound wave as it decreases with distance from its source, because the energy of the wave is spread over a larger and larger area. The intensity decreases as it moves away from the speaker, as discussed in Waves . The energy is also absorbed by objects and converted into thermal energy by the viscosity of the air. In addition, during each compression, a little heat transfers to the air; during each rarefaction, even less heat transfers from the air, and these heat transfers reduce the organized disturbance into random thermal motions. Whether the heat transfer from compression to rarefaction is significant depends on how far apart they are—that is, it depends on wavelength. Wavelength, frequency, amplitude, and speed of propagation are important characteristics for sound, as they are for all waves.

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Sound Waves
Speed Of Sound Propagation

Speed of Sound

A sound wave is fundamentally a pressure disturbance that propagates through a medium by particle interaction. In other words, sound waves move through a physical medium by alternately contracting and expanding the section of the medium in which it propagates. The rate at which the sound waves propagate through the medium is known as the speed of sound. In this article, you will discover the definition and factors affecting the speed of sound.

Speed of Sound Definition

The speed of sound is defined as the distance through which a sound wave’s point, such as a compression or a rarefaction, travels per unit of time. The speed of sound remains the same for all frequencies in a given medium under the same physical conditions.

Speed of Sound Formula

Since the speed of sound is the distance travelled by the sound wave in a given time, the speed of sound can be determined by the following formula:

v = λ f

Where v is the velocity, λ is the wavelength of the sound wave, and f is the frequency.

The relationship between the speed of sound, its frequency, and wavelength is the same as for all waves. The wavelength of a sound is the distance between adjacent compressions or rarefactions . The frequency is the same as the source’s and is the number of waves that pass a point per unit time.

Solved Example:

How long does it take for a sound wave of frequency 2 kHz and a wavelength of 35 cm to travel a distance of 1.5 km?

We know that the speed of sound is given by the formula:

v = λ ν

Substituting the values in the equation, we get

v = 0.35 m × 2000 Hz = 700 m/s

The time taken by the sound wave to travel a distance of 1.5 km can be calculated as follows:

Time = Distance Travelled/ Velocity

Time = 1500 m/ 700 m/s = 2.1 s

Factors Affecting the Speed of Sound

Density and temperature of the medium in which the sound wave travels affect the speed of sound.

Density of the Medium

When the medium is dense, the molecules in the medium are closely packed, which means that the sound travels faster. Therefore, the speed of sound increases as the density of the medium increases.

Temperature of the Medium

The speed of sound is directly proportional to the temperature. Therefore, as the temperature increases, the speed of sound increases.

Speed of Sound in Different Media

The speed of the sound depends on the density and the elasticity of the medium through which it travels. In general, sound travels faster in liquids than in gases and quicker in solids than in liquids. The greater the elasticity and the lower the density, the faster sound travels in a medium.

Speed of Sound in Solid

Sound is nothing more than a disturbance propagated by the collisions between the particles, one molecule hitting the next and so forth. Solids are significantly denser than liquids or gases, and this means that the molecules are closer to each other in solids than in liquids and liquids than in gases. This closeness due to density means that they can collide very quickly. Effectively it takes less time for a molecule of a solid to bump into its neighbouring molecule. Due to this advantage, the velocity of sound in a solid is faster than in a gas.

The speed of sound in solid is 6000 metres per second, while the speed of sound in steel is equal to 5100 metres per second. Another interesting fact about the speed of sound is that sound travels 35 times faster in diamonds than in the air.

Speed of Sound in Liquid

Speed of Sound in Water

The speed of sound in water is more than that of the air, and sound travels faster in water than in the air. The speed of sound in water is 1480 metres per second. It is also interesting that the speed may vary between 1450 to 1498 metres per second in distilled water. In contrast, seawater’s speed is 1531 metres per second when the temperature is between 20 o C to 25 o C.

Speed of Sound in Gas

We should remember that the speed of sound is independent of the density of the medium when it enters a liquid or solid. Since gases expand to fill the given space, density is relatively uniform irrespective of gas type, which isn’t the case with solids and liquids. The velocity of sound in gases is proportional to the square root of the absolute temperature (measured in Kelvin). Still, it is independent of the frequency of the sound wave or the pressure and the density of the medium. But none of the gases we find in real life is ideal gases , and this causes the properties to change slightly. The velocity of sound in air at 20 o C is 343.2 m/s which translates to 1,236 km/h.

Speed of Sound in Vacuum

The speed of sound in a vacuum is zero metres per second, as there are no particles present in the vacuum. The sound waves travel in a medium when there are particles for the propagation of these sound waves. Since the vacuum is an empty space, there is no propagation of sound waves.

Table of Speed of Sound in Various Mediums

Another very curious fact is that in solids, sound waves can be created either by compression or by tearing of the solid, also known as Shearing. Such waves exhibit different properties from each other and also travel at different speeds. This effect is seen clearly in Earthquakes. Earthquakes are created due to the movement of the earth’s plates, which then send these disturbances in the form of waves similar to sound waves through the earth and to the surface, causing an Earthquake. Typically compression waves travel faster than tearing waves, so Earthquakes always start with an up-and-down motion, followed after some time by a side-to-side motion. In seismic terms, the compression waves are called P-waves, and the tearing waves are called S-waves . They are the more destructive of the two, causing most of the damage in an earthquake.

Visualise sound waves like never before with the help of animations provided in the video

Frequently Asked Questions – FAQs

What is the speed of sound in vacuum, name the property used for distinguishing a sharp sound from a dull sound., define the intensity of sound., how does the speed of sound depend on the elasticity of the medium, why is the speed of sound maximum in solids, name the factors on which the speed of sound in a gas depends., what is a sonic boom, the below video helps to completely revise the chapter sound class 9.

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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.

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Speed of Sound: How Sound Travels Through Objects and Materials

Posted by Acoustical Surfaces on 03/14/2024 11:54 am | Leave a Comment

From the snap of a twig to the booming echo of a drumbeat, sound plays an important role in helping us navigate our space. While sound is incredibly important, many people rarely stop to ponder its physical properties.

In physics, sound is defined as an acoustic vibration that sends waves through a medium, such as a solid, liquid, or gas. 1 These mediums’ properties can influence sound’s speed. By understanding the relation between material properties and the speed of sound, you can optimize the acoustics of various spaces, from professional recording studios to company conference rooms.

We’ll be diving into the fascinating mechanics of sound propagation and explain how different objects’ density, elasticity, and temperature all influence the speed of sound (plus how to contain or absorb those fast-moving sound waves).

Table of Contents

What is the Formula for the Speed of Sound?

Many people assume that the speed of sound is a constant number, but this isn’t the case. The materials that transmit sound can influence its speed considerably. Even so, there is a general speed of sound formula, which multiplies the sound’s wavelength by its frequency. 2 In mathematical terms:

In this formula:

v represents the speed of sound
f is the frequency of the sound wave
λ is the length of the sound wave

While this general formula is an excellent baseline, the speed of sound can vary greatly from one medium to the next, depending on its temperature, density, and elasticity.

Speed of Sound: Example Equation

To clarify the connection between the sound’s speed, frequency, and wavelength, let’s take a look at a real-life example.

Let’s say that you’re measuring a sound with a frequency of 261 Hz, also known as middle C or concert pitch. 3 This sound’s wavelength is around 1.3 meters. After plugging these numbers into the speed of sound formula, you can calculate sound using the following equation:

v=(261 Hz)(1.3 m)

v=341.9 m/s

With this equation in mind, let’s take a closer look at the role of various materials’ properties on the speed of sound.

How Does a Material’s Density Impact the Speed of Sound?

Density, which measures the mass per unit volume of a given material, can influence the speed of sound significantly. That’s because density dictates how closely a material’s molecules are packed together.

Since sound is kinesthetic energy that travels by passing from one molecule to the next, materials with more densely packed molecules facilitate faster sound propagation. For this reason, sound travels faster through solids than liquids and faster through liquids than gasses.

Varying Densities of Different Elements

Denser elements often feature heavier molecules, which take more energy to vibrate, subsequently slowing down sound’s speed. As a result, sound can travel through aluminum nearly twice as fast as it moves through gold, due to the differences in the molecules. 4

How Does Material Density Relate to Soundproofing?

If you’re interested in optimizing the acoustics of a space, you’ll likely employ soundproofing solutions at some point. Soundproofing materials add mass to walls and ceilings to prevent sound from escaping.

Since these materials are often quite dense, it begs the question, “Why use dense, solid materials for soundproofing if sound waves travel through them faster?”

When dense materials are thick enough, they contain enough molecules to drain the sound wave of energy before it can reach the other side. That’s why most soundproofing solutions, from double-layer drywall to solid-core doors, are so thick.

How Does a Material’s Elasticity Impact the Speed of Sound?

Another key factor that influences the speed of sound through materials is their elasticity, which refers to a material’s ability to maintain its shape when placed under stress. For example, a rigid material like steel won’t lose its shape as easily as a more flexible material like rubber.

Materials with atoms that are strongly attracted to each other end up being more rigid, due to their powerful internal bonds. The strength of these bonds ultimately determines how quickly a material will return to its original shape.

So, what does this mean for the speed of sound? Particles that quickly regain their shape after an external force will also vibrate at higher speeds. As a result, they enable sound to travel faster than materials with lower elastic properties. 4

Contact us to find your perfect acoustical fit today!

Speed of Sound Elasticity Equation

If you want to flex your mathematical muscles, you can calculate the speed of sound while taking into account different material’s elastic properties.

This more complicated formula divides the elastic property by the inertial property and takes the resulting number’s square root, as showcased by this equation 2 :

Here’s a quick breakdown:

Elastic property is a material’s ability to deform and reform in the face of an external force.
Inertial property looks at whether a material will stay at rest or in motion in the absence of an external force.

How Does a Material’s Temperature Impact the Speed of Sound?

Many people are often surprised to learn that temperature can influence the speed of sound. Typically, higher temperatures facilitate faster sound travel, especially through gasses.

So, what’s behind this phenomenon? Well, heat is a form of kinetic energy. Increasing the temperature speeds up the vibration of molecules within a material, and causes sound waves to jump from one molecule to the next more quickly.

This explains why room-temperature air has a speed of sound of 346 m/s, while air at water’s freezing point (0°C / 32°F) has a speed of sound of 331 m/s. 4 While this fascinating connection between thermal dynamics and acoustics is often overlooked, it can make a noteworthy difference in a room’s sound quality.

Speed of Sound Formula With Temperature

If you want to measure the average speed of sound for various temperatures, you can use this formula 5 :

v = 331 m/s + 0.61T

Here’s how the equation breaks down:

v is the speed of sound
331 m/s is the speed of sound at 0°C
0.61 is a constant that represents the increase in sound’s speed with every additional degree
T is the air’s temperature in Celcius

What is the Speed of Sound for Common Materials?

Now that you understand the basic components that affect the speed of sound, let’s take a look at how quickly sound moves through the following mediums 2 :

Gasses at 0°C or 32°F

Air – 331 m/s
Carbon dioxide – 259 m/s
Oxygen – 316 m/s
Helium – 965 m/s
Hydrogen – 1,290 m/s

Liquids at 20°C or 68°F

Ethanol – 1,160 m/s
Mercury – 1,450 m/s
Freshwater – 1,480 m/s
Sea water – 1,540 m/s
Rubber – 60 m/s
Polyethylene – 920 m/s
Lead – 1,210 m/s
Gold – 3,240 m/s
Marble – 3,810 m/s
Copper – 4,600 m/s
Aluminum – 5,120 m/s
Iron – 5,120 m/s
Glass – 5,640 m/s
Steel – 5,960 m/s
Diamond – 12,000 m/s

As you can see, the effect of these materials’ varying properties on the speed of sound is quite pronounced—sound travels nearly 35 times faster through a diamond than it does through air. 6

Soundproofing Solutions

The speed of sound is a complex and fascinating phenomenon, but thankfully, soundproofing solutions tend to be relatively simple.

Here are some popular soundproofing solutions we offer at Acoustical Surfaces:

Noise S.T.O.P.™ Vinyl Barrier Mass Loaded Vinyl Barrier
Noise S.T.O.P.™ Interior Soundproof Glass Window
SoundBreak XP Acoustically Enhanced Gypsum Boar d
Green Glue Viscoelastic Damping Compound
Resilient Sound Isolation Clips (RSICs)

Sound Absorption Solutions

Soundproofing solutions have many valuable applications, but they’re not always right for your acoustical goals. Maybe you want to enhance the acoustics of a space instead, whether that involves dampening distracting echoes and reverberations or balancing the sound within a space. In this case, sound absorption is what you need.

While soundproofing materials isolate sound within a space, sound absorption materials are often soft and foamy, enabling them to soak up excess sound waves like a sponge and stop them from bouncing around, creating an unpleasant cacophony in their wake.

Some of our best-selling sound absorption products at Acoustical Surfaces are:

Poly Max™ Acoustical Panels
Envirocoustic™ Wood Wool Cementitious Wood-Fiber Acoustic Ceiling and Wall Panels
Echo Eliminator Bonded Acoustical Cotton Panels
NOISE S.T.O.P. Fabric-Wrapped Acoustical Panels
Flat Faced Open Cell Melamine Acoustical Foam
WALLMATE® Fabric Wall System

Learn More About Sound With Acoustical Surfaces

From music to meteorology, the speed of sound is an important concept. It’s especially relevant to understand how sound speeds change with varying levels of density, elasticity, and temperature.

By understanding the way sound travels through different materials, you can make smarter acoustical decisions. However, you don’t have to navigate this process alone—just reach out to our team of sound experts at Acoustical Surfaces . We’ve been providing comprehensive sound solutions for over 35 years.

If you want custom sound solutions for your space, whether that’s a classroom, restaurant, recording studio, or home, we can help you select the ideal products. Contact our team today to receive tailored soundproofing or sound absorption support.

BYJU’s. Sound Waves. https://byjus.com/physics/sound-waves/
LibreTexts. 17.3: Speed of Sound. https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/17%3A_Sound/17.03%3A_Speed_of_Sound
SFU. Wavelength. https://www.sfu.ca/sonic-studio-webdav/handbook/Wavelength.html
Iowa State University. Sound. https://www.nde-ed.org/Physics/Sound/index.xhtml
University of Rhode Island. Sound Waves. https://penrose.uri.edu/labs/PHY275/sound_waves/sound_waves.pdf
Inspirit. Speed Of Sound Study Guide. https://www.inspiritvr.com/speed-of-sound-study-guide/

Additional Resources

Creating better-sounding rooms.

Solutions to Common Noise Problems

CAD, CSI, & Revit Library

Speed of Sound in Solids

Claudia Tiller, Spring 2023

This page discusses the speed of sound in various solids, how to calculate them, and examples of such calculations.

1 The Main Idea
2.1 A Mathematical Model
2.2 Speeds of Various Compositions
3.1 Theoretical
3.2 Numerical Example
4 Connectedness
6.1 Further reading
6.2 External links
7 References

The Main Idea

The speed of sound can be defines as the distance travelled per a unit of time by a sound wave as it travels through an elastic medium. Elasticity refers to the ability of a body to resist distorting influence and return to its original shape when that influence is removed.

Factors that control the speed that sound travels in solids is measured by the solid's density and elasticity, as they affect the vibrational energy of the sound. Overall, the way the solid is composed determines the sound's speed limit through that solid.

The Structure of Solids and Effects on Sound Travel

Mediums are composed of particles that can be closely knit together or spread apart. Solids are characterized by an arrangement of atoms, ions, or molecules, where these components are generally locked in their positions. The particles can also be defined as elastic or inelastic. Particles that are closer to each other allow sound to be transferred quicker through the medium. Since particles that are compressed closer together allow sound to travel faster, it can be reasoned that sound travels slower in air.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it.

The practicality of this concept is highly applicable. The human ear captures sound waves through the outer cartilage of the ear, called the Pinna. The sound waves then travel up the ear canal and arrive at the ear drum which vibrates from the sound waves. After traveling through the inner ear, the vibrations arrive at the Cochlea. The Cochlea transfers the vibrations into information that auditory nerves can analyze.

A Mathematical Model

The speed of sound in solids [math]\displaystyle{ {V_{s}} }[/math] can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

[math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math]

Alternative speed equation:

[math]\displaystyle{ {V_{s}} = \sqrt{\frac{B}{\rho}} }[/math]

[math]\displaystyle{ ρ }[/math] = density

[math]\displaystyle{ B }[/math] = Bulks Modulus

Bulks Modulus = [math]\displaystyle{ {\frac {ΔP}{ΔV/V}} }[/math]

[math]\displaystyle{ d }[/math] = interatomic bond length

[math]\displaystyle{ K_{s} }[/math] = Interatomic bond stiffness

Youngs Modulus = ( [math]\displaystyle{ Y = K_{s}/d }[/math] )

Youngs Modulus: [math]\displaystyle{ Y ={\frac{Stress}{Strain}} }[/math]

[math]\displaystyle{ Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} }[/math]

[math]\displaystyle{ Strain = {\frac{ΔL_{wire}}{L_{0}}} }[/math]

Speeds of Various Compositions

Theoretical

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, [math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math] , you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

[math]\displaystyle{ d \cdot \sqrt{\frac{4 \cdot K_{s}}{m_{atom}}} = d \cdot \sqrt{\frac{4 \cdot K_{s}}{m_{atom}}} }[/math] After simplification [math]\displaystyle{ V_{s_{1}} = V_{s{2}} }[/math]

Numerical Example

The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that Youngs Modulus = ( [math]\displaystyle{ K_{s}/d }[/math] ). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for d , we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass ( [math]\displaystyle{ V=m*d }[/math] ), we can find d , since d is equal to the cube root of volume.

Once d is solved for, it can be plugged back into the the equation [math]\displaystyle{ Y = K_{s}/d }[/math] to solve for [math]\displaystyle{ K_{s} }[/math]

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. [math]\displaystyle{ m_{atom} = }[/math] atomic mass / [math]\displaystyle{ 6.022e23 }[/math]

Now that all variables are solved for, we can substitute values into our [math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math] equation.

[math]\displaystyle{ {V_{s}} = 1.6 \cdot 10^{-10} \cdot \sqrt{ \frac{78534.7}{1.79 \cdot 10^{-22}}} }[/math]

[math]\displaystyle{ {V_{s}} = 2723 }[/math] m/s

Connectedness

Computing the speed of sound in solids depends on a mass' interatomic properties, such as interatomic bond length. In this specific case, an object's elasticity depends on the interatomic bond length. There are many applications that connect to the ability to compute the speed of sounds.

Seismic and ultrasonic imaging are also fields that benefit greatly from the calculation of sound speeds in solids. Seismic imaging refers to capturing images of the subsurface structure of the Earth. Seismic waves can be generated by earthquakes or other sources. Engineers and scientists can then locate gas and oil reservoirs, monitor activity such as volcano eruptions, and geological formations. In ultrasonic imaging, ultrasonic waves can be sent through the body and have the time it takes to bounce back be measured. This then creates images of internal organs or tissues, used in cases such as prenatal imaging as well as medical diagnosing. In more specific fields such as in Industrial Engineering, these calculations could be applied to questions regarding how to build a soundproof area. It would therefore be optimal to select a solid with a low speed of sound velocity, with a solid that has tightly packed particles. There are many vast applications to this, as an object's ability to block or allow sound waves through it. However, some cases require contractors to build structures that allow sound to travel through. Material testing uses the calculation of sound in solids to determine mechanical properties of such materials. Engineers can then calculate the material's elasticity, stiffness, and other properties. Knowledge regarding how solids are structured and how they correlate with the speed of sounds in those solids are vital to building structures that meet the criteria.

Overall, being able to calculate the speed of sounds in solids has a wide range of applications in engineering, medicine, and science.

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

Youngs Modulus: [1] Interatomic Bonds: [2]

External links

Internet resources on this topic can be found at:

Engineering Tool Box [3]

Hyperphysics [4]

Potto Project [5]

NDT Resource Center [6]

The Engineering ToolBox [7]

Ear Image [8]

Yew Chung [9]

This section contains the the references used while writing this page

Chart from [10]

Matter and Interactions 4th Edition by Chabay and Sherwood

Wikipage created by Daiven Patel

What Is the Speed of Sound?

The speed of sound varies depending on the temperature of the air through which the sound moves.

On Earth, the speed of sound at sea level — assuming an air temperature of 59 degrees Fahrenheit (15 degrees Celsius) — is 761.2 mph (1,225 km/h).

Because gas molecules move more slowly at colder temperatures, that slows the speed of sound; sound moves faster through warmer air. Therefore, the speed required to break the sound barrier decreases higher in the atmosphere, where temperatures are colder.

Scientists are interested in the speed of sound, according to NASA, because it indicates the speed of transmitting a "small disturbance" (another way of describing a sound wave) through a gas medium.

The transmission of the disturbance takes place as molecules in the gas hit each other. The speed of sound also varies depending on the type of gas (air, pure oxygen, carbon dioxide, etc.) through which the sound moves.

The first controlled flight to break the speed of sound — also known as Mach 1 — took place Oct. 14, 1947, when test pilot Chuck Yeager breached the barrier using Glamorous Glennis, an X-1 aircraft.

NASA's X-43A aircraft flew more than nine times as fast on Nov. 16, 2004, flying Mach 9.6 or almost 7,000 mph. That stands as the fastest speed achieved to date by a jet-powered aircraft.

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Speed of Sound Calculator

Table of contents

This speed of sound calculator determines the speed of sound in the air and water .

Not everybody knows about the sound speed dependence on the temperature – the higher the air temperature, the faster the sound can propagate.

To calculate the speed of sound in water , just choose the temperature – Fahrenheit °F or Celsius °C. You can also choose the desired unit – with this tool, you can find the speed of sound in mph, ft/s, or even knots!

Speed of sound in air

Air is almost an ideal gas. The formula for the speed of sound in ideal gases is:

c c c – Speed of sound in an ideal gas;
R R R – Molar gas constant, approximately 8.3145 J·mol −1 ·K −1 ;
γ \gamma γ – Adiabatic index, approximately 1.4 for air;
T T T – Absolute temperature; and
M M M – The molar mass of the gas. For dry air is about 0.0289645 kg/mol

Substituting the values for air, we have the simplified formula for the speed of sound in m/s:

where T T T is in °C.

Did you notice something interesting? The speed of sound in the gas depends only on two constants – γ \gamma γ and R R R – and on the temperature but not on the air pressure or density, as it is sometimes claimed. The humidity of air also has an effect on the speed of sound, but the influence is so small that it can be neglected. The temperature is the only important factor!

Speed of sound in water

The most often used value is 1482 m/s (for 20 °C); however, an easy formula for the speed of sound in water doesn't exist. Many authors derived equations from experimental data, but the equations are complicated, and they always contain higher-order polynomials and plenty of coefficients.

The data in our calculator for speed in water comes from the speed of sound in water charts . The speed of sound in water is an important parameter in sonar research and acoustical oceanography. Nevertheless, the formula for seawater is even more complex as the speed of sound is also changing with the salinity.

💡 How about the speed of sound in solids? Well, our speed of sound in solids calculator can help you calculate it.

How to use the speed of sound calculator?

Let's calculate how the sound propagates in cold water – like really cold, from wintering swimming activities.

Choose the section you need – the speed of sound in water or air . It's water in our case, so we will use the bottom part of the calculator.

Pick the temperature unit . Let's take degrees Fahrenheit.

Select the temperature from a drop-down list . Take this freezingly cold 40 °F.

The speed of sound calculator displays the speed of sound in water ; it's 4672 ft/s.

Let's compare it with 90 °F (warm bath temperature). The speed is equal to 4960 ft/s this time. Remember that you can always change the units of speed of sound: mph, ft/s, m/s, km/h, even to knots if you wish to.

Now, as you know the speed, calculate the time or distance with this speed calculator . Also, you can check how far the storm is with our lightning distance calculator – the speed of sound in air is a significant factor for that calculations.

How do I calculate the speed of sound in air given temperature?

To determine the speed of sound in air, follow these steps:

If you're given the air temperature in °C or °F, you need to first convert it to kelvins .
Add 1 to the temperature in kelvins and take the square root .
Multiply the result from Step 2 by 331.3 .
You've just determined the speed of sound in the air in m/s – congrats!

How does the speed of sound change with temperature?

The speed of sound increases as the air temperature increases. The precise formula is:

c_air = 331.3 × √(1 + T/273.15) ,

where T is the air temperature in °C. This formula returns speed in m/s.

What is the speed of sound in air?

Assuming the air temperature of 20 °C, the speed of sound is:

343.14 m/s;
1235.3 km/h;
1125.8 ft/s; or

You can derive these results by applying the formula c_air = 331.3 × √(1 + T/273.15) , where T = 20°C. The result is in m/s, and then, if needed, you have to convert it to other speed units.

What is the speed of sound in water?

Assuming the water temperature of 20 °C, the speed of sound is:

4859 ft/s; or

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16.2: Traveling Waves

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Learning Objectives

Describe the basic characteristics of wave motion
Define the terms wavelength, amplitude, period, frequency, and wave speed
Explain the difference between longitudinal and transverse waves, and give examples of each type
List the different types of waves

We saw in Oscillations that oscillatory motion is an important type of behavior that can be used to model a wide range of physical phenomena. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion (Figure $\PageIndex{1}$).

Types of Waves

A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves.

Basic mechanical waves are governed by Newton’s laws and require a medium. A medium is the substance a mechanical waves propagates through, and the medium produces an elastic restoring force when it is deformed. Mechanical waves transfer energy and momentum, without transferring mass. Some examples of mechanical waves are water waves, sound waves, and seismic waves. The medium for water waves is water; for sound waves, the medium is usually air. (Sound waves can travel in other media as well; we will look at that in more detail in Sound .) For surface water waves, the disturbance occurs on the surface of the water, perhaps created by a rock thrown into a pond or by a swimmer splashing the surface repeatedly. For sound waves, the disturbance is a change in air pressure, perhaps created by the oscillating cone inside a speaker or a vibrating tuning fork. In both cases, the disturbance is the oscillation of the molecules of the fluid. In mechanical waves, energy and momentum transfer with the motion of the wave, whereas the mass oscillates around an equilibrium point. (We discuss this in Energy and Power of a Wave .) Earthquakes generate seismic waves from several types of disturbances, including the disturbance of Earth’s surface and pressure disturbances under the surface. Seismic waves travel through the solids and liquids that form Earth. In this chapter, we focus on mechanical waves.

Electromagnetic waves are associated with oscillations in electric and magnetic fields and do not require a medium. Examples include gamma rays, X-rays, ultraviolet waves, visible light, infrared waves, microwaves, and radio waves. Electromagnetic waves can travel through a vacuum at the speed of light, v = c = 2.99792458 x 10 8 m/s. For example, light from distant stars travels through the vacuum of space and reaches Earth. Electromagnetic waves have some characteristics that are similar to mechanical waves; they are covered in more detail in Electromagnetic Waves .

Matter waves are a central part of the branch of physics known as quantum mechanics. These waves are associated with protons, electrons, neutrons, and other fundamental particles found in nature. The theory that all types of matter have wavelike properties was first proposed by Louis de Broglie in 1924. Matter waves are discussed in Photons and Matter Waves .

Mechanical Waves

Mechanical waves exhibit characteristics common to all waves, such as amplitude, wavelength, period, frequency, and energy. All wave characteristics can be described by a small set of underlying principles.

The simplest mechanical waves repeat themselves for several cycles and are associated with simple harmonic motion. These simple harmonic waves can be modeled using some combination of sine and cosine functions. For example, consider the simplified surface water wave that moves across the surface of water as illustrated in Figure $\PageIndex{2}$. Unlike complex ocean waves, in surface water waves, the medium, in this case water, moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. In Figure $\PageIndex{2}$, the waves causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs (peaks and valleys) pass under the bird. The crest is the highest point of the wave, and the trough is the lowest part of the wave. The time for one complete oscillation of the up-and-down motion is the wave’s period T. The wave’s frequency is the number of waves that pass through a point per unit time and is equal to f = $\frac{1}{T}$. The period can be expressed using any convenient unit of time but is usually measured in seconds; frequency is usually measured in hertz (Hz), where 1 Hz = 1 s −1 .

The length of the wave is called the wavelength and is represented by the Greek letter lambda ($\lambda$), which is measured in any convenient unit of length, such as a centimeter or meter. The wavelength can be measured between any two similar points along the medium that have the same height and the same slope. In Figure $\PageIndex{2}$, the wavelength is shown measured between two crests. As stated above, the period of the wave is equal to the time for one oscillation, but it is also equal to the time for one wavelength to pass through a point along the wave’s path.

The amplitude of the wave (A) is a measure of the maximum displacement of the medium from its equilibrium position. In the figure, the equilibrium position is indicated by the dotted line, which is the height of the water if there were no waves moving through it. In this case, the wave is symmetrical, the crest of the wave is a distance +A above the equilibrium position, and the trough is a distance −A below the equilibrium position. The units for the amplitude can be centimeters or meters, or any convenient unit of distance.

Figure shows a wave with the equilibrium position marked with a horizontal line. The vertical distance from the line to the crest of the wave is labeled x and that from the line to the trough is labeled minus x. There is a bird shown bobbing up and down in the wave. The vertical distance that the bird travels is labeled 2x. The horizontal distance between two consecutive crests is labeled lambda. A vector pointing right is labeled v subscript w.

The water wave in the figure moves through the medium with a propagation velocity $\vec{v}$. The magnitude of the wave velocity is the distance the wave travels in a given time, which is one wavelength in the time of one period, and the wave speed is the magnitude of wave velocity. In equation form, this is

\[v = \frac{\lambda}{T} = \lambda f \ldotp \label{16.1}\]

This fundamental relationship holds for all types of waves. For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.

Transverse and Longitudinal Waves

We have seen that a simple mechanical wave consists of a periodic disturbance that propagates from one place to another through a medium. In Figure $\PageIndex{3}$(a), the wave propagates in the horizontal direction, whereas the medium is disturbed in the vertical direction. Such a wave is called a transverse wave . In a transverse wave, the wave may propagate in any direction, but the disturbance of the medium is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. Figure $\PageIndex{3}$(b) shows an example of a longitudinal wave. The size of the disturbance is its amplitude A and is completely independent of the speed of propagation v.

Figure a, labeled transverse wave, shows a person holding one end of a long, horizontally placed spring and moving it up and down. The spring forms a wave which propagates away from the person. This is labeled transverse wave. The vertical distance between the crest of the wave and the equilibrium position of the spring is labeled A. Figure b, labeled longitudinal wave, shows the person moving the spring to and fro horizontally. The spring is compressed and elongated alternately. This is labeled longitudinal wave. The horizontal distance from the middle of one compression to the middle of one rarefaction is labeled A.

A simple graphical representation of a section of the spring shown in Figure $\PageIndex{3}$(b) is shown in Figure $\PageIndex{4}$. Figure $\PageIndex{4}$(a) shows the equilibrium position of the spring before any waves move down it. A point on the spring is marked with a blue dot. Figure $\PageIndex{4}$(b) through (g) show snapshots of the spring taken one-quarter of a period apart, sometime after the end of` the spring is oscillated back and forth in the x-direction at a constant frequency. The disturbance of the wave is seen as the compressions and the expansions of the spring. Note that the blue dot oscillates around its equilibrium position a distance A, as the longitudinal wave moves in the positive x-direction with a constant speed. The distance A is the amplitude of the wave. The y-position of the dot does not change as the wave moves through the spring. The wavelength of the wave is measured in part (d). The wavelength depends on the speed of the wave and the frequency of the driving force.

Figures a through g show different stages of a longitudinal wave passing through a spring. A blue dot marks a point on the spring. This moves from left to right as the wave propagates towards the right. In figure b at time t=0, the dot is to the right of the equilibrium position. In figure d, at time t equal to half T, the dot is to the left of the equilibrium position. In figure f, at time t=T, the dot is again to the right. The distance between the equilibrium position and the extreme left or right position of the dot is the same and is labeled A. The distance between two identical parts of the wave is labeled lambda.

Figure $\PageIndex{4}$: (a) This is a simple, graphical representation of a section of the stretched spring shown in Figure $\PageIndex{3}$(b), representing the spring’s equilibrium position before any waves are induced on the spring. A point on the spring is marked by a blue dot. (b–g) Longitudinal waves are created by oscillating the end of the spring (not shown) back and forth along the x-axis. The longitudinal wave, with a wavelength $\lambda$, moves along the spring in the +x-direction with a wave speed v. For convenience, the wavelength is measured in (d). Note that the point on the spring that was marked with the blue dot moves back and forth a distance A from the equilibrium position, oscillating around the equilibrium position of the point.

Waves may be transverse, longitudinal, or a combination of the two. Examples of transverse waves are the waves on stringed instruments or surface waves on water, such as ripples moving on a pond. Sound waves in air and water are longitudinal. With sound waves, the disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and for this reason, the sound waves in them are longitudinal waves. Sound in solids can have both longitudinal and transverse components, such as those in a seismic wave. Earthquakes generate seismic waves under Earth’s surface with both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). The components of seismic waves have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water. Ocean waves also have both transverse and longitudinal components.

Example 16.1: Wave on a String

A student takes a 30.00-m-long string and attaches one end to the wall in the physics lab. The student then holds the free end of the rope, keeping the tension constant in the rope. The student then begins to send waves down the string by moving the end of the string up and down with a frequency of 2.00 Hz. The maximum displacement of the end of the string is 20.00 cm. The first wave hits the lab wall 6.00 s after it was created. (a) What is the speed of the wave? (b) What is the period of the wave? (c) What is the wavelength of the wave?

The speed of the wave can be derived by dividing the distance traveled by the time.
The period of the wave is the inverse of the frequency of the driving force.
The wavelength can be found from the speed and the period v = $\frac{\lambda}{T}$.
The first wave traveled 30.00 m in 6.00 s: $$v = \frac{30.00\; m}{6.00\; s} = 5.00\; m/s \ldotp$$
. The period is equal to the inverse of the frequency: $$T = \frac{1}{f} = \frac{1}{2.00\; s^{-1}} = 0.50\; s \ldotp$$
The wavelength is equal to the velocity times the period: $$\lambda = vT = (5.00\; m/s)(0.50\; s) = 2.50\; m \ldotp$$

Significance

The frequency of the wave produced by an oscillating driving force is equal to the frequency of the driving force.

Exercise 16.1

g When a guitar string is plucked, the guitar string oscillates as a result of waves moving through the string. The vibrations of the string cause the air molecules to oscillate, forming sound waves. The frequency of the sound waves is equal to the frequency of the vibrating string. Is the wavelength of the sound wave always equal to the wavelength of the waves on the string?

Example 16.2: Characteristics of a Wave

A transverse mechanical wave propagates in the positive x-direction through a spring (as shown in Figure $\PageIndex{3}$(a)) with a constant wave speed, and the medium oscillates between +A and −A around an equilibrium position. The graph in Figure $\PageIndex{5}$ shows the height of the spring (y) versus the position (x), where the xaxis points in the direction of propagation. The figure shows the height of the spring versus the x-position at t = 0.00 s as a dotted line and the wave at t = 3.00 s as a solid line. (a) Determine the wavelength and amplitude of the wave. (b) Find the propagation velocity of the wave. (c) Calculate the period and frequency of the wave.

Figure shows two transverse waves whose y values vary from -6 cm to 6 cm. One wave, marked t=0 seconds is shown as a dotted line. It has crests at x equal to 2, 10 and 18 cm. The other wave, marked t=3 seconds is shown as a solid line. It has crests at x equal to 0, 8 and 16 cm.

The amplitude and wavelength can be determined from the graph.
Since the velocity is constant, the velocity of the wave can be found by dividing the distance traveled by the wave by the time it took the wave to travel the distance.
The period can be found from v = $\frac{\lambda}{T}$ and the frequency from f = $\frac{1}{T}$.
Read the wavelength from the graph, looking at the purple arrow in Figure $\PageIndex{6}$. Read the amplitude by looking at the green arrow. The wavelength is $\lambda$ = 8.00 cm and the amplitude is A = 6.00 cm.

The distance the wave traveled from time t = 0.00 s to time t = 3.00 s can be seen in the graph. Consider the red arrow, which shows the distance the crest has moved in 3 s. The distance is 8.00 cm − 2.00 cm = 6.00 cm. The velocity is $$v = \frac{\Delta x}{\Delta t} = \frac{8.00\; cm - 2.00\; cm}{3.00\; s - 0.00\; s} = 2.00\; cm/s \ldotp$$
The period is T = $\frac{\lambda}{v}$ = $\frac{8.00\; cm}{2.00\; cm/s}$ = 4.00\; s and the frequency is f = $\frac{1}{T}$ = $\frac{1}{4.00\; s}$ = 0.25 Hz.

Note that the wavelength can be found using any two successive identical points that repeat, having the same height and slope. You should choose two points that are most convenient. The displacement can also be found using any convenient point.

Exercise 16.2

The propagation velocity of a transverse or longitudinal mechanical wave may be constant as the wave disturbance moves through the medium. Consider a transverse mechanical wave: Is the velocity of the medium also constant?

FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

TeachEngineering
Traveling Sound

Hands-on Activity Traveling Sound

Grade Level: 4 (3-5)

Time Required: 30 minutes

Expendable Cost/Group: US $2.00

Group Size: 2

Activity Dependency: None

Subject Areas: Physical Science, Reasoning and Proof, Science and Technology

NGSS Performance Expectations:

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

Seeing and Feeling Sound Vibrations
Pitch and Frequency
Sound Visualization Stations

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Engineering connection, learning objectives, materials list, worksheets and attachments, more curriculum like this, pre-req knowledge, introduction/motivation, vocabulary/definitions, troubleshooting tips, activity extensions, activity scaling, user comments & tips.

Sound and acoustic engineers know that the shape of a room and its materials greatly impact how sound waves travel. Recording studios are designed in soundproof booths so that the recorded music does not contain any unwanted external noise. Libraries are designed to reduce any introduced noises, to assure a quiet, non-distracting learning environment. Concert halls are designed so that sound generated on the stage travels to the back of the space without being distorted.

After this activity, students should be able to:

Explain that sound can move through solids, liquids and gases.
Describe how sound needs molecules to move and that changing the medium that it travels through changes the sound.
Describe how engineers use sound energy when designing spaces, such as movie theaters.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science, international technology and engineering educators association - technology.

View aligned curriculum

Do you agree with this alignment? Thanks for your feedback!

State Standards

Colorado - science.

Each group needs:

large bowl (metal works best)
2 metal objects, such as spoons, to knock together
Traveling Sound Worksheet , one per student

A basic understanding of the phases of matter: liquids, solids and gases.

Sound engineers are especially interested in the way sound travels. Can you hear as well when you sit in the back of the class as when you sit in the front? What about in the assembly hall or gymnasium? On the playground? Can you think of other times when you cannot hear as well as someone else? What happened? How about in a movie theater? What do engineers do so that the sound quality is good for everyone in a movie theater? (Possible answers: Add speakers around the room, curtains, carpet the walls, cone-shaped theaters act like a megaphone and help to direct sound waves further.)

Which is louder—walking on carpet or on tile? It is quieter on carpet because the carpet absorbs the sound energy . Sound energy, light energy and other types of energy, need molecules to travel through and vibrate , but sometimes sound energy is absorbed by an object or material. Engineers use this idea when designing rooms that are meant to be quiet. Have you ever noticed how the walls of a movie theater are covered with carpet or fabric? This is to prevent echoing of the sound system. Sometimes when you are in an empty room, your voice echoes or sounds hollow. This is because an empty room has no materials in it that might absorb the sound energy, so the sound bounces off the hard walls, back at you. This makes it hard to hear clearly.

Do you think sound energy can travel through air? Of course it can! That is how sound energy travels when you talk to a friend. How about water? Can you hear sound travel under water? How about a solid? Can sound move through a solid object? Engineers want to know if sound can travel through solids, liquids and gases so they can develop ways to send messages to people all over the world. Can you imagine how great sound would be if it could travel anywhere?

Understanding the properties of sound and how sound waves travel helps engineers determine the best room shape and construction materials when designing libraries, classrooms, sound recording studios, concert halls and theatres. Room shape and materials can impact how sound waves travel since sound waves bounce off different object in different ways. In this activity, we are going to study how sound waves travel through liquids, solids and gases, and think about how engineers might use this information.

Before the Activity

Gather materials and make copies of the Traveling Sound Worksheet .
Divide the class into teams of two students each.

With the Students

Ask the students to predict if sound can move through solids, liquids and gases.
Have the students complete the worksheet, which leads them through traveling sound wave activities.
Can sound energy travel through solids? Students place their ears on a desk or table as they tap or scratch on the top. They compare that to the same sound made when their ear is not pressed to the table.
Can sound energy traveling through liquids? Fill a large bowl or bucket (metal works best) with water. One student taps two spoons together under the water. Two other students observe and compare the tapping sound they hear, as heard through the air and as heard by placing an ear against the bowl.
Can sound energy traveling through gases (air)? The students feel their throats gently during each of these tasks:
Hum with your mouth and nose open.
Hum with your mouth open and nose closed.
Hum with your mouth closed and nose open.
Hum with your mouth and nose closed.
Discuss with the students what happened. Were their predictions correct? Can sound travel through air, water and solids? (Answer: Yes!) Sound needs molecules to move. Solids, liquids and gases are all made of molecules. The characteristics of the molecules (for example, the space between the molecules) determine whether the sound becomes muffled or changes in some way.
How might engineers use the knowledge that sound travels through solids, liquids and gases? (Possible answers: Engineers create devices that send sound anywhere — through water to a submarine in the ocean, through wires to your TV, and through the air in surround sound movie theaters or emergency broadcast signals.)

echo: Repetition of a sound by reflection of sound waves from a surface.

frequency: The rate of vibrations in different pitches.

pitch: The highness or lowness of a sound.

sound energy: Audible energy that is released when you talk, play musical instruments or slam a door.

sound wave: A longitudinal pressure wave of audible or inaudible sound.

vibration: When something moves back and forth, it is said to vibrate. Sound is made by vibrations that are usually too fast to see.

volume: When sound becomes louder or softer.

wave: A disturbance that travels through a medium, such as air or water.

Pre-Activity Assessment

Prediction: Ask students if they think sound can move through solid, liquid, and gas. If so what are some examples? (Possible examples: Students may recall talking under water or using tin can and string telephones.)

Activity Embedded Assessment

Worksheet: Have students use the Traveling Sounds Worksheet to guide them in the activity and as a place to record their observations. Review their answers to gauge their mastery of the subject.

Post-Activity Assessment

Toss-a-Question: Ask students to independently think of an answer to the question below and write it on a half sheet of paper. Have students wad up and toss the paper to another team member who then adds their answer idea. After all students have written down ideas, have them toss the paper wad to another team, who reads the answers aloud to the class. Discuss answers with the class.

What is an example of something through which sound can travel?

Neighbor Check: Have the students compare their activity observations with a neighbor. Are they the same or different? Have each team report some of their similar and dissimilar observations to the rest of the class.

Engineering Design: The supply of air on Earth is running out! Several futuristic cities for human habitation are being designed either underwater or deep inside mountains. Have each student group become a city planning engineering team and draw a communication system for sending emergency messages between the new cities. Make sure to illustrate and describe how the sound energy (message) will move through air, water or solid rock.

This activity can be very loud. Ask students to not disturb others while they learn and have fun.

To bring some humor to the activity, ask each student to hum a small part of their favorite song while feeling their throat. Have each student alternate between having their nose and mouth open or closed while humming non-stop. Why does the sound change depending on whether you close your nose or mouth? What happens if you block your ears? What does this activity teach us about sound? (Answer: Sound vibrations must travel through air for us to hear them. Like a musical instrument [perhaps a recorder or flute], if you change the holes where sound escapes, it changes the pitch, but not the frequency/vibrations of the sound.)

If a metal bowl is used during the activity, the vibrations from the objects colliding underwater vibrate the bowl, creating the illusion that the bowl is being struck. Have students draw the vibrations in the bowl on a piece of paper. Do the vibrations change if the objects are tapped together increasing softly?

Have students think about different forms of communications. Does sound travel most often through solids, liquids or gases? Have students poll their friends, family and neighbors to solicit their ideas.

For lower grades, conduct the activities as a class instead of in teams. Younger students could also draw pictures of their observations instead of writing in sentence form.

Students are introduced to the sound environment as an important aspect of a room or building. Several examples of acoustical engineering design for varied environments are presented.

preview of 'Sound Environment Shapers' Lesson

Students learn how different materials reflect and absorb sound.

preview of 'To Absorb or Reflect... That is the Question' Lesson

Students learn that sound is energy and has the ability to do work. Students discover that sound is produced by a vibration and they observe soundwaves and how they travel through mediums. They understand that sound can be absorbed, reflected or transmitted.

preview of 'Decibels and Acoustical Engineering' Lesson

Students use the engineering design process to design and create soundproof rooms that use only one type of material. They learn and explore about how these different materials react to sound by absorbing or reflecting sound and then test their theories using a box as a proxy for a soundproof room. ...

preview of 'What Soundproofing Material Works Best? ' Activity

Dictionary.com. Lexico Publishing Group, LLC. Accessed December 19, 2005. (Source of some vocabulary definitions, with some adaptation.) http://www.dictionary.com

Contributors

Supporting program, acknowledgements.

The contents of this digital library curriculum were developed under grants from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation (GK-12 grant no. 0338326). However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: March 17, 2021

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Airlines + Airports

The 10 Fastest Planes in the World

Non-military planes, that is.

Urbanandsport/NurPhoto via Getty Images

For nearly 30 years, travelers could fly faster than sound. Thanks to the iconic Concorde supersonic jet, which cruised at 1,350 mph, transatlantic flights could take less than three hours — that's about twice as fast as commercial flights today. But Concorde was retired in 2003, and commercial air travel isn't nearly as fast as it used to be. But if you fly private , you can get pretty close to Mach 1 (767 mph), the speed of sound.

Here are the fastest non-military jets in the world that will get you from A to B as quickly as possible.

Cessna Citation X+ (717 mph)

The fastest private jet in the world, the Cessna Citation X+ is capable of speeds as fast as Mach 0.935. However, its range is somewhat limited as far as private jets go: 3,460 nautical miles, or just enough to make it between New York and Western Europe. The aircraft was introduced in 2012 as an update to the Cessna Citation X, which has been in service since 1996. The plane might not hold its title for much longer, though — the upcoming Bombardier Global 8000 is anticipated to fly at Mach 0.94, or 721 mph.

Gulfstream G700 (710 mph)

SeongJoon Cho/Bloomberg via Getty Images

Reaching Mach 0.925, or 710 mph, the G700 is Gulfstream's newest aircraft, with a range of 7,500 nautical miles. That means it can fly from New York to Johannesburg or from Los Angeles to Sydney. The G800, however, is due to launch later this year, and while it'll have the same speed, its range will be 8,000 nautical miles.

Gulfstream G650 (710 mph)

Marcus Brandt/picture alliance via Getty Images

Like its cousin, the G700, Gulfstream's G650 flies at Mach 0.925, or 710 mph. Its range is a bit shorter, at 7,000 nautical miles — though that's still enough to fly between New York and Tokyo and Los Angeles and Auckland.

Gulfstream G650ER (710 mph)

Carla Gottgens/Bloomberg via Getty Images

The ER in G650ER stands for "extended range," so while you'll fly just as fast as you would in a G650 (that is, Mach 0.925, or 710 mph), you'll be able to fly farther. The G650ER has a range of 7,500 nautical miles, just like the G700.

Gulfstream G600 (691 mph)

Mark Elias/Bloomberg via Getty Images

If there's something Gulfstream does well, it's consistency, at least when it comes to speed. Yes, here is yet another Gulfstream jet that flies up to Mach 0.925, or 710 mph. Its range is 6,600 nautical miles, which is enough to connect New York and Dubai or Los Angeles and Sydney.

Gulfstream G500 (710 mph)

Jason Alden/Bloomberg via Getty Images

You've probably already guessed it — the G500 flies at Mach 0.925, or 710 mph. You might also have inferred that its range is less than that of its brethren, and you'd be right again. Gulfstream's G500 has a range of 5,300 nautical miles, so it can fly from New York to Buenos Aires or Los Angeles to Tokyo.

Bombardier Global 7500 (710 mph)

Graham Hughes/Bloomberg via Getty Images

As you can tell, Mach 0.925, or 710 mph, seems to be something of a sweet spot with private jets. Bombardier's Global 7500 flies at this speed like many other aircraft, but it has an industry-leading range (until the Global 8000 enters service) of 7,700 nautical miles.

Bombardier Global 6500 (691 mph)

Bridget Bennett/Bloomberg via Getty Images

Taking an ever-so-slight step down in speed, the Bombardier Global 6500 reaches Mach 0.9, or 691 mph, at cruising altitude. With a range of 6,600 nautical miles, it can fly nonstop between New York and Dubai or Los Angeles and Sydney.

Dassault Falcon 8X (691 mph)

Jerod Harris/Getty Images

Until the Falcon 10X enters service (likely in 2027), Dassault's fastest and farthest-flying private jet is the 8X, which can travel 6,450 nautical miles at speeds up to Mach 0.9, or 691 mph. That covers New York to Nairobi or London to Jakarta.

Dassault Falcon 7X (691 mph)

PATRICK BERNARD/AFP via Getty Images

The Falcon 8X's predecessor, the Falcon 7X, was the first private jet with fly-by-wire capabilities. It, like its successor, flies at Mach 0.9, or 691 mph, though it has a smaller range of 5,950 nautical miles. That's enough for a nonstop flight between New York and Tokyo or London and Singapore.

Honorable Mention: Boeing 747-8 (656 mph)

Chona Kasinger/Bloomberg via Getty Images

If you're wondering which commercial aircraft is the fastest, that title goes to the Boeing 747-8, which flies at Mach 0.855, or 652 mph. Though the 747 is no longer in production, Lufthansa, Korean Air, and Air China still fly these planes — they have an impressive range of 8,000 nautical miles, which is farther than any private jet on this list.

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A sound wave of frequency 245 Hz travels with the speed of $300\dfrac{m}{s}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave? A. $Y = 0.03\sin \left[5.1x - \left(0.2 \times {10^3}t\right)\right]$ B. $Y = 0.06\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$ C. $Y = 0.06\sin \left[0.8x - \left(0.5 \times {10^3}t\right)\right]$ D. $Y = 0.03\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$

Question Answer
A Sound Wave Of Frequency 245 Hz Travels With

Unveiling The Secrets Behind The Concorde's Record-Breaking Flights

W hen a plane like the Concorde Jet is ahead of its time and doesn't ultimately last, it's more than simply a defunct project, it's a failed promise of the future, of what could have been. There was once a supersonic passenger jet that could travel faster than the speed of sound and cut half the flight time off routes, but today we still only have regular, non-supersonic flights. It's the same feeling you get when stepping off one of those moving walkways at the airport.

The Concorde was essentially a record-breaking machine. It could achieve speeds of 1,354 mph , otherwise known as Mach 2.04, which is more than twice the speed of sound. In 1996, that's what enabled it to traverse from New York City to London in a paltry two hours and 53 minutes, a record that Guinness labeled the "fastest flight across the Atlantic in a commercial aircraft." This isn't to suggest that every flight it offered passengers would regularly achieve such record-breaking speeds, but every aspect of its design was streamlined with an eye toward really fast flights.

Read more: The 10 Most Iconic Airplanes In Aviation History, Ranked

Where That Innovative Speed Came From

A rare collaboration between the French and British aviation industries, the idea behind the Concorde was to significantly reduce long-haul flights in key routes around the world. It certainly did. It was powered by four afterburner-equipped Olympus 593 Mk610 turbojet engines, an engine technology often reserved for military jets and found on Avro Vulcan strategic bombers . Like those bombers, the Concorde had the ability to travel at altitudes upwards of 60,000 ft , meaning it encountered thinner air and less drag than lower, traditional commercial flights.

The Concorde managed to even look fast while parked, and there was a reason for that. Every part of the aircraft –- from the adjustable, downward-turned nose to the stretched-out body to the curved wings – was streamlined to reduce drag and increase flying speed. Those delta-wings (once again similar to the Avro Vulcan) were set at a 55-degree angle with the fuselage, reducing drag along a body designed to absorb the impact of shockwaves while traveling at supersonic speeds.

When it comes to the record-breaking transatlantic flight, the time achieved was more than due to the aforementioned design specs, as Simple Flying notes . It was planned that way by everyone involved, including Captain Leslie Scott, First Officer Tim Orchard, and Engineering Officer Rick Eades. They apparently chose February for its ideal upper air temperature and wind velocity, and achieved Mach 2 quickly and for as long as possible during the flight. Additionally, while the approaching runway at Heathrow usually had flights arriving from the east, the Concorde was coming from the west and convinced air traffic controllers to let them land that way to preserve the record-breaking flight time. It's safe to say that such considerations aren't usually made for other flights that don't break records.

Why It Came To An End

Building, operating, and maintaining such an advanced aircraft came with exceedingly high costs , which seemingly hamstrung the program from the start. Work on the aircraft exceeded $2 billion, over four times the initial estimate, and the aircraft consumed around 6,770 gallons of fuel per hour of flight, about double the amount of the giant Airbus A380, according to How Stuff Works . These high production and maintenance costs came against inevitable high ticket costs that were out of reach for the average passenger, often between $12,000 to $14,000 for a roundtrip ticket .

Then in July 2000, an Air France Concorde departed Paris's DeGaulle airport for New York, when one of the engines caught fire and caused the aircraft to crash in France, killing all 109 passengers aboard, as well as four people on the ground. After a year-long grounding by the FAA, the Concorde's last commercial flight came in 2003, with the 100 celebrity-laden passengers spending upwards of $60,000 for a roundtrip ticket from JFK to Heathrow.

While supersonic commercial flights remain highly costly and impractical for the immediate future, the Concorde's innovation continues to make waves in the airline industry, in the hopes of mainstreaming commercial supersonic speeds that are both convenient and safe for passengers seeking to arrive a little sooner. American company Boom Supersonic hopes for its Overture SST to reach this with the 75% less cost, and last year CNN reported that European company Destinus was targeting hypersonic flights between Dubai and Memphis. Where this all goes remains to be seen, yet perhaps one day it'll take us to a time when we're no longer romanticizing the Concorde because we have something better. But that'll probably take a while.

Read the original article on SlashGear

What is the speed of light?

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

graphic representing the speed of light showing lines of light of different colors; blue, green, yellow and white.

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?

Galileo Galilei is credited with discovering the first four moons of Jupiter.

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.

Dr. Albert A. Michelson stands next to a large tube supported by wooden beams.

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

Albert Einstein writing on a blackboard.

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?

A sparkling diamond amongst dark coal-like rock.

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 .

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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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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The Science Behind the Sound at the Gorge Amphitheatre

By Seth Sommerfeld June 6, 2024 Published in the Summer 2024 issue of Seattle Met

Image: Nestor Salgado/shutterstock.com

While the music of Washington artists resonates around the world, there may be no better place in the world to hear live music resonate than a remote outpost smack dab between Seattle and Spokane. Overlooking the Columbia River basin in George, Washington, the Gorge Amphitheatre continually gets recognition as one of the best outdoor music venues on the planet. Once a modest space, opened by Vince and Carol Bryan in 1986 to draw folks to their adjoining Champs de Brionne winery, it has since blossomed into a hot spot for superstar summer concerts and blowout weekend festivals. No venue comes close to matching the Gorge’s pristine natural beauty, and despite being a wide, open-air space, it’s consistently one of the best- sounding outdoor venues around . How is that even possible?

To get the lowdown on the venue’s sonic quirks, we talked to team members at Carlson Audio Systems, the Seattle audio equipment specialists who’ve worked the Gorge for shows ranging from Brandi Carlile and the Dave Matthews Band to the Watershed and Sasquatch! (#RIP) festivals.

Sound Mapping

Image: courtesy Carlson Audio Systems

An aerial view of the Gorge makes it clear that the lawn at the top of the hill actually isn’t squared to the stage—the southeast lawn is farther from the stage than the southwest. This puts everything at odd angles and distances that the sound crew must compensate for by adding more speakers.

The technology in line array speakers has greatly advanced in the digital era. The sound teams can use software to map out hot spots and quiet spots, allowing them to test out design systems from the comfort of a Seattle office and then having only to fine-tune smaller specifics once at the Gorge.

The Speed of Sound

Because the Gorge is so vast, adjustments must be made to keep things sounding right farther from the stage. Carlson employs delay systems. Microphones measure specific testing tones to calculate what delay in the speed of sound is needed to use on additional speakers to sync with the stage action. The result is seamless.

20-Foot Ramp

One of the trickiest elements for sound engineering teams at the Gorge is its unique setup for loading in gear. The load-in area behind the stage is at a much lower elevation than the stage itself, so everything must be painstakingly hauled up a 20-foot ramp.

The Changeover

Artists have their own sound engineers. Carlson’s Jesse Turner says it’s a mark of pride when tweaks are minimal: “you hand over the keys to a PA to an engineer, if he spends an hour working on getting it to sound the way he wants it to versus if he spends 15 minutes.”

Controlled Noise

Image: laviddichterman/flickr CC

Festival Setup

For anyone who’s attended a festival at the Gorge with multiple stages, it’s always a marvel how little sound bleed there seems to be with various acts playing at the same time. According to Carlson director of personnel Morgan Hodge, the sheer elevation change from the main stage to the top of the hill protects the sound from clashing together—it almost blows over the top, like how wind might travel.

It may seem overly obvious, but the remoteness of the Gorge has its sonic benefits. There’s basically no nearby noise pollution, and the openness of the space prevents any harsh slapback echo effects. Plus, sound engineers can crank up the volume because there’s nobody around to complain. “You can be pretty much as loud as you want to be,” says Turner.

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Speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 m/s (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or 1 km in 2.91 s or one mile in 4.69 s.It depends strongly on temperature as well as the medium through which a sound wave is propagating.
17.3: Speed of Sound
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 ...
Physics Tutorial: The Speed of Sound
In equation form, this is. speed = distance/time. 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.
Speed of Sound (video)
In non-humid air at 20 degrees Celsius, the speed of sound is about 343 meters per second or 767 miles per hour. We can also watch the speed of sound of a repeating simple harmonic wave. The speed of the wave can again be determined by the speed of the compressed regions as they travel through the medium.
Speed of Sound in Physics
Speed of Sound in Physics. This entry was posted on June 17, 2023 by Anne Helmenstine (updated on June 22, 2023) The speed of sound in dry air at room temperature is 343 m/s or 1125 ft/s. In physics, the speed of sound is the distance traveled per unit of time by a sound wave through a medium. It is highest for stiff solids and lowest for gases.
14.1 Speed of Sound, Frequency, and Wavelength
The relationship between the speed of sound, its frequency, and wavelength is the same as for all waves: v = fλ, v = f λ, 14.1. 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 ...
Speed of Sound
The speed of sound is the distance traveled over time by a sound wave in an elastic medium. The SI unit of speed is meters per second or (m/s). The speed of sound in dry air at 20 ° C is 343.2 m/s. In different mediums (gas, solids, or liquids) the speed of sound is different than 343.2 m/s. ... If sound travels faster in certain solids, this ...
17.2: Speed of Sound, Frequency, and Wavelength
The relationship of the speed of sound vw, its frequency f, and its wavelength λ is given by vw = fλ, which is the same relationship given for all waves. In air, the speed of sound is related to air temperature T by vw = (331m / s)√ T 273K. vw is the same for all frequencies and wavelengths.
17.2 Speed of Sound
Speed of Sound in Various Media. Table 17.1 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.
Relative speed of sound in solids, liquids, and gases
For instance, if you heat up the air that a sound wave is travelling through, the density of the air decreases. This explains why sound travels faster through hotter air compared to colder air. The speed of sound at 20 degrees Celsius is about 343 meters per second, but the speed of sound at zero degrees Celsius is only about 331 meters per second.
17.1 Sound Waves
The physical phenomenon of sound is a disturbance of matter that is transmitted from its source outward. ... 16.1 Traveling Waves; 16.2 Mathematics of Waves; 16.3 Wave Speed on a ... Additional Problems; Challenge Problems; 17 Sound. Introduction; 17.1 Sound Waves; 17.2 Speed of Sound; 17.3 Sound Intensity; 17.4 Normal Modes of a Standing Sound ...
The Speed of Sound & How does Sound Travel? A Fundamental ...
Sound moves incredibly fast! You snap your fingers, and it can be heard almost instantly throughout an entire room. But how does sound travel so quickly? ...
Speed of sound
sound. speed of sound, speed at which sound waves propagate through different materials. In particular, for dry air at a temperature of 0 °C (32 °F), the modern value for the speed of sound is 331.29 metres (1,086.9 feet) per second. The speed of sound in liquid water at 8 °C (46 °F) is about 1,439 metres (4,721 feet) per second.
Speed of Sound
the speed of sound is m/s = ft/s = mi/hr. This calculation is usually accurate enough for dry air, but for great precision one must examine the more general relationship for sound speed in gases. If you measured sound speed in your oven, you would find that this relationship doesn't fit. At 200°C this relationship gives 453 m/s while the more ...
Explanation, Speed of Sound in Different Media, FAQs
Solution: We know that the speed of sound is given by the formula: v = λ ν. Substituting the values in the equation, we get. v = 0.35 m × 2000 Hz = 700 m/s. The time taken by the sound wave to travel a distance of 1.5 km can be calculated as follows: Time = Distance Travelled/ Velocity.
Sound
Sound waves travel through the air as squashed-up compressions and stretched-out rarefactions. They only look like this on an oscilloscope trace. Why instruments sound different. ... The speed of sound in air (at sea level) is about 1220 km/h (760 mph or 340 meters per second). Compared to light waves, sound waves creep along at a snail's pace ...
Traveling sound waves
The speed of sound increases by about 6 m/s if the temperature increases by 10 o C. Sound travels faster in liquids and solids than in gases, since the particles in liquids and solids are closer together and can respond more quickly to the motion of their neighbors. The speed of sound in water is ~1500 m/s, in iron it is ~5000 m/s.
Speed of Sound: How Sound Travels Through Objects and Materials
Copper - 4,600 m/s. Aluminum - 5,120 m/s. Iron - 5,120 m/s. Glass - 5,640 m/s. Steel - 5,960 m/s. Diamond - 12,000 m/s. As you can see, the effect of these materials' varying properties on the speed of sound is quite pronounced—sound travels nearly 35 times faster through a diamond than it does through air. 6.
Speed of Sound in Solids
The speed of sound in solids V s can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length. V s = d ⋅ K s m a t o m. Alternative speed equation:
What Is the Speed of Sound
The speed of sound varies depending on the temperature of the air through which the sound moves. On Earth, the speed of sound at sea level — assuming an air temperature of 59 degrees Fahrenheit ...
Speed of Sound Calculator
The speed of sound calculator displays the speed of sound in water; it's 4672 ft/s. Let's compare it with 90 °F (warm bath temperature). The speed is equal to 4960 ft/s this time. Remember that you can always change the units of speed of sound: mph, ft/s, m/s, km/h, even to knots if you wish to.
16.2: Traveling Waves
Electromagnetic waves can travel through a vacuum at the speed of light, v = c = 2.99792458 x 10 8 m/s. For example, light from distant stars travels through the vacuum of space and reaches Earth. ... For water waves, v is the speed of a surface wave; for sound, v is the speed of sound; and for visible light, v is the speed of light.
Traveling Sound
Students explore how sound waves move through liquids, solids and gases in a series of simple sound energy experiments. Understanding the properties of sound and how sound waves travel helps engineers determine the best room shape and construction materials when designing sound recording studios, classrooms, libraries, concert halls and theatres.
10 Fastest Planes in the World in 2024
Until the Falcon 10X enters service (likely in 2027), Dassault's fastest and farthest-flying private jet is the 8X, which can travel 6,450 nautical miles at speeds up to Mach 0.9, or 691 mph. That ...
A sound wave of frequency 245 Hz travels with the speed class ...
A sound wave of frequency 245 Hz travels with the speed class 11 physics JEE_Main. A sound wave of frequency 245 Hz travels with the speed of 300m s along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
Unveiling The Secrets Behind The Concorde's Record-Breaking Flights
The Concorde was essentially a record-breaking machine. It could achieve speeds of 1,354 mph, otherwise known as Mach 2.04, which is more than twice the speed of sound.In 1996, that's what enabled ...
How fast does light travel?
The speed of light traveling through a vacuum is exactly 299,792,458 meters (983,571,056 feet) per second. ... On Sense and the Sensible, arguing that light, unlike sound and smell, must be ...
The Science Behind the Sound at the Gorge Amphitheatre
The Speed of Sound. Because the Gorge is so vast, adjustments must be made to keep things sounding right farther from the stage. Carlson employs delay systems. Microphones measure specific testing tones to calculate what delay in the speed of sound is needed to use on additional speakers to sync with the stage action. The result is seamless. On ...
SpaceX launches Starship rocket. See it fly faster than the speed of sound
Published 9:32 AM EDT, Thu June 6, 2024. Link Copied! Video Ad Feedback. SpaceX launches Starship rocket. See it fly faster than the speed of sound. SpaceX launched its Starship, the most powerful ...
Razer BlackShark V2 HyperSpeed
Surround Sound: THX Spatial Audio: THX Spatial Audio: 7.1 Surround Sound: 7.1 Surround Sound: Connectivity: Razer™ HyperSpeed Wireless Technology (2.4 GHz) + Bluetooth 5.2: Wireless: Razer™ HyperSpeed Wireless Technology (2.4 GHz) + Bluetooth 5.2 Wired: USB Type-A: USB Type-A: 3.5mm Analog: Battery Life: up to 70 hours: up to 70 hours ...

Factors Affecting Wave Speed

The Speed of Sound in Air

Look It Up!

The Wave Equation Revisited

Check Your Understanding

Speed of Sound in Physics

What Is the Speed of Sound?

Mach Numher

Solids, Liquids, and Gases

The Hot Chocolate Effect

Speed of Sound Formulas

Factors That Affect the Speed of Sound

Speed of Sound on Mars

Speed of Sound Example Problems

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Physics library

Relative speed of sound in solids, liquids, and gases

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Video transcript

17.1 Sound Waves

Interactive

Models Describing Sound

Speed of Sound

Speed of Sound Definition

Speed of Sound Formula

Factors Affecting the Speed of Sound

Density of the Medium

Temperature of the Medium

Speed of Sound in Different Media

Speed of Sound in Solid

Speed of Sound in Liquid

Speed of Sound in Water

Speed of Sound in Gas

Speed of Sound in Vacuum

Table of Speed of Sound in Various Mediums

Visualise sound waves like never before with the help of animations provided in the video

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Speed of Sound: How Sound Travels Through Objects and Materials

What is the Formula for the Speed of Sound?

Speed of Sound: Example Equation

How Does a Material’s Density Impact the Speed of Sound?

Varying Densities of Different Elements

How Does Material Density Relate to Soundproofing?

How Does a Material’s Elasticity Impact the Speed of Sound?

Speed of Sound Elasticity Equation

How Does a Material’s Temperature Impact the Speed of Sound?

Speed of Sound Formula With Temperature

What is the Speed of Sound for Common Materials?

Gasses at 0°C or 32°F

Liquids at 20°C or 68°F

Soundproofing Solutions

Sound Absorption Solutions

Learn More About Sound With Acoustical Surfaces

Additional Resources

Solutions to Common Noise Problems

CAD, CSI, & Revit Library

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Speed of Sound in Solids

The Main Idea

The Structure of Solids and Effects on Sound Travel

A Mathematical Model

Speeds of Various Compositions

Theoretical

Numerical Example

Connectedness