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

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

What is sound?

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

Robert Boyle's classic experiment

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

How sound travels

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

The science of sound waves

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

Whispering galleries and amphitheaters

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

Measuring waves

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

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

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

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

How to measure the speed of sound

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

• Electric guitars
• Speech synthesis
• Synthesizers

On other sites

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

Educational books for younger readers

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

Popular science

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

Academic books

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

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

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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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12.2: Speed of Sound

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Has this ever happened to you? You see a flash of lightning on the horizon, but several seconds pass before you hear the rumble of thunder. The reason? The speed of light is much faster than the speed of sound.

What Is the Speed of Sound?

The speed of sound is the distance that sound waves travel in a given amount of time. You’ll often see the speed of sound given as 343 meters per second. But that’s just the speed of sound under a certain set of conditions, specifically, through dry air at 20 °C. The speed of sound may be very different through other matter or at other temperatures.

Speed of Sound in Different Media

Sound waves are mechanical waves, and mechanical waves can only travel through matter. The matter through which the waves travel is called the medium (plural, media). The Table below gives the speed of sound in several different media. Generally, sound waves travel most quickly through solids, followed by liquids, and then by gases. Particles of matter are closest together in solids and farthest apart in gases. When particles are closer together, they can more quickly pass the energy of vibrations to nearby particles.

Q: The table gives the speed of sound in dry air. Do you think that sound travels more or less quickly through air that contains water vapor? (Hint: Compare the speed of sound in water and air in the table.)

A: Sound travels at a higher speed through water than air, so it travels more quickly through air that contains water vapor than it does through dry air.

Temperature and Speed of Sound

The speed of sound also depends on the temperature of the medium. For a given medium, sound has a slower speed at lower temperatures. You can compare the speed of sound in dry air at different temperatures in the following Table below. At a lower temperature, particles of the medium are moving more slowly, so it takes them longer to transfer the energy of the sound waves.

Q: What do you think the speed of sound might be in dry air at a temperature of -20 °C?

A: For each 1 degree Celsius that temperature decreases, the speed of sound decreases by 0.6 m/s. So sound travels through dry, -20 °C air at a speed of 319 m/s.

Can you calculate the speed of sound in air and the wave speed on the string in the Violin simulation below? Use the Wavelength vs Frequency graph on the top left to analyze the waves produced by the violin. The product of the wavelength and frequency can be used to determine the speed of sound in air and wave speed on the violin string:

Interactive Element

• The speed of sound is the distance that sound waves travel in a given amount of time. The speed of sound in dry air at 20 °C is 343 meters per second.
• Generally, sound waves travel most quickly through solids, followed by liquids, and then by gases.
• For a given medium, sound waves travel more slowly at lower temperatures.
• What is the speed of sound in dry air at 20 °C?
• Describe variation in the speed of sound through various media.
• Explain how temperature affects the speed of sound.

Additional Resources

Real World Application: Tracking the Storm

Study Guide: Waves Study Guide

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17.2: Speed of Sound, Frequency, and Wavelength

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Learning Objectives

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

• Define pitch.
• Describe the relationship between the speed of sound, its frequency, and its wavelength.
• Describe the effects on the speed of sound as it travels through various media.
• Describe the effects of temperature on the speed of sound.

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display. The flash of an explosion is seen well before its sound is heard, implying both that sound travels at a finite speed and that it is much slower than light. You can also directly sense the frequency of a sound. Perception of frequency is called pitch . The wavelength of sound is not directly sensed, but indirect evidence is found in the correlation of the size of musical instruments with their pitch. Small instruments, such as a piccolo, typically make high-pitch sounds, while large instruments, such as a tuba, typically make low-pitch sounds. High pitch means small wavelength, and the size of a musical instrument is directly related to the wavelengths of sound it produces. So a small instrument creates short-wavelength sounds. Similar arguments hold that a large instrument creates long-wavelength sounds.

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

\[v_w = f\lambda,\]

where \(v_w\) is the speed of sound, \(f\) is its frequency, and \(\lambda\) is its wavelength. The wavelength of a sound is the distance between adjacent identical parts of a wave—for example, between adjacent compressions as illustrated in Figure \(\PageIndex{2}\). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Table \(\PageIndex{1}\) makes it apparent that the speed of sound varies greatly in different media. The speed of sound in a medium is determined by a combination of the medium’s rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound. For materials that have similar rigidities, sound will travel faster through the one with the lower density because the sound energy is more easily transferred from particle to particle. The speed of sound in air is low, because air is compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Earthquakes, essentially sound waves in Earth’s crust, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes have both longitudinal and transverse components, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both components of earthquakes travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves correspondingly range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake.

The speed of sound is affected by temperature in a given medium. For air at sea level, the speed of sound is given by

\[v_w = (331 \, m/s)\sqrt{\dfrac{T}{273 \, K}},\]

where the temperature (denoted as \(T\)) is in units of kelvin. The speed of sound in gases is related to the average speed of particles in the gas, \(v_{rms}\), and that

\[v_{rms} = \sqrt{\dfrac{3 \, kT}{m}},\]

where \(k\) is the Boltzmann constant \((1.38 \times 10^{-23} \, J/K)\) and \(m\) is the mass of each (identical) particle in the gas. So, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At \(0^oC\), the speed of sound is 331 m/s, whereas at \(20^oC\) it is 343 m/s, less than a 4% increase. Figure \(\PageIndex{3}\) shows a use of the speed of sound by a bat to sense distances. Echoes are also used in medical imaging.

One of the more important properties of sound is that its speed is nearly independent of frequency. This independence is certainly true in open air for sounds in the audible range of 20 to 20,000 Hz. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, and so all frequencies must travel at nearly the same speed. Recall that

\[v_w = f\lambda.\]

In a given medium under fixed conditions, \(v_w\) is constant, so that there is a relationship between \(f\) and \(\lambda\); the higher the frequency, the smaller the wavelength. See Figure \(\PageIndex{4}\) and consider the following example.

Example \(\PageIndex{1}\): Calculating Wavelengths: What Are the Wavelengths of Audible Sounds?

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

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

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

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

The speed of sound can change when sound travels from one medium to another. However, the frequency usually remains the same because it is like a driven oscillation and has the frequency of the original source. If \(v_w\) changes and \(f\) remains the same, then the wavelength \(\lambda\) must change. That is, because \(v_w = f\lambda\), the higher the speed of a sound, the greater its wavelength for a given frequency.

MAKING CONNECTIONS: TAKE-HOME INVESTIGATION - VOICE AS A SOUND WAVE

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

Exercise \(\PageIndex{1A}\)

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

Sound and light both travel at definite speeds. The speed of sound is slower than the speed of light. The first firework is probably very close by, so the speed difference is not noticeable. The second firework is farther away, so the light arrives at your eyes noticeably sooner than the sound wave arrives at your ears.

Exercise \(\PageIndex{1B}\)

You observe two musical instruments that you cannot identify. One plays high-pitch sounds and the other plays low-pitch sounds. How could you determine which is which without hearing either of them play?

Compare their sizes. High-pitch instruments are generally smaller than low-pitch instruments because they generate a smaller wavelength.

• The relationship of the speed of sound \(v_w\), its frequency \(f\), and its wavelength \(\lambda\) is given by \(v_w = f\lambda,\) which is the same relationship given for all waves.
• In air, the speed of sound is related to air temperature \(T\) by \(v_w = (331 \, m/s) \sqrt{\dfrac{T}{273 \, K}}.\) \(v_w\) is the same for all frequencies and wavelengths.

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Traveling waves

17 How sound moves

Speed of sound.

There’s a delay between when a sound is created and when it is heard. In everyday life, the delay is usually too short to notice. However, the delay can be noticeable if the distance between source and detector is large enough. You see lightning before you hear the thunder. If you’ve sat in the outfield seats in a baseball stadium, you’ve experienced the delay between seeing the player hit the ball and the sound of the “whack.” Life experiences tell us that sound travels fast, but not nearly as fast as light does. Careful experiments confirm this idea.

The speed of sound in air is roughly 340 m/s. The actual value depends somewhat on the temperature and humidity. In everyday terms, sound travels about the length of three and a half foot ball fields every second- about 50% faster than a Boeing 747 (roughly 250 m/s). This may seem fast, but it’s tiny compared to light, which travels roughly a million times faster than sound (roughly 300,000,000 m/s).

Sound requires some material in which to propagate (i.e. travel). This material sound travels through is called the medium . You can show that sound requires a medium by putting a cell phone inside a glass jar connected to a vacuum pump. As the air is removed from the jar, the cell phone’s ringer gets quieter and quieter. A youTube video (2:05 min) produced by the UNSW PhysClips project shows the demo with a drumming toy monkey [1] instead of a cell phone.

What affects the speed of sound?

Sound travels at different speeds though different materials. The physical properties of the medium are the only factors that affect the speed of sound- nothing else matters.

The speed of sound in a material is determined mainly by two properties- the stiffness of the material and the density of the material. Sound travels fastest through materials that are stiff and light. In general, sound travels fastest through solids, slower through liquids and slowest through gasses. (See the table on this page). This may seem backwards- after all, metals are quite dense. However, the high density of metals is more than offset by far greater stiffness (compared to liquids and solids).

The speed of sound in air depends mainly on temperature. The speed of sound is 331 m/s in dry air at 0 o Celsius and increases slightly with temperature- about 0.6 m/s for every 1 o Celsius for temperatures commonly found on Earth. Though speed of sound in air also depends on humidity, the effect is tiny- sound travels only about 1 m/s faster in air with 100% humidity air at 20 o C than it does in completely dry air at the same temperature.

Nothing else matters

The properties of the medium are the only factors that affect the speed of sound- nothing else matters.

Frequency of the sound does not matter- high frequency sounds travel at the same speed as low frequency sounds. If you’ve ever listened to music, you’ve witnessed this-  the low notes and the high notes that were made simultaneously reach you simultaneously, even if you are far from the stage. If you’ve heard someone shout from across a field, you’ve noticed that the entire shout sound (which contains many different frequencies at once) reaches you at the same time. If different frequencies traveled at different rates, some frequencies would arrive before others.

The amplitude of the sound does not matter- loud sounds and quiet ones travel at the same speed. Whisper or yell- it doesn’t matter. The sound still takes the same amount of time to reach the listener.  You’ve probably heard that you can figure out how far away the lightning by counting the seconds between when you see lightning and hear thunder. If the speed of sound depended on loudness, this rule of thumb would have to account for loudness- yet there is nothing in the rule about loud vs. quiet thunder. The rule of thumb works the same for all thunder- regardless of loudness . That’s because the speed of sound doesn’t depend on amplitude.

Stop to thinks

• Which takes longer to cross a football field: the sound of a high pitched chirp emitted by a fruit bat or the (relatively) low pitched sound emitted by a trumpet?
• Which sound takes longer to travel 100 meters: the sound of a snapping twig in the forest or the sound of a gunshot?
• Which takes longer to travel the distance of a football field: the low pitched sound of a whale or the somewhat higher pitched sound of a human being?

Constant speed

Sound travels at a constant speed. Sound does not speed up or slow down as it travels (unless the properties of the material the sound is going through changes). I know what you’re thinking- how is that possible? Sounds die out as they travel, right? True. That means sounds must slow down and come to a stop, right? Wrong. As sound travels, its amplitude decreases- but that’s not the same thing as slowing down. Sound (in air) covers roughly 340 meters each and every second, even as its amplitude shrinks. Eventually, the amplitude gets small enough that the sound is undetectable. A sound’s amplitude shrinks as it travels, but its speed remains constant.

The basic equation for constant speed motion (shown below) applies to sound.

[latex]d=vt[/latex]

In this equation, [latex]d[/latex] represents the distance traveled by the sound, [latex]t[/latex] represents the amount of time it took to go that distance and [latex]v[/latex] represents the speed.

Rule of thumb for lightning example

Example: thunder and lightning.

The rule of thumb for figuring out how far away a lightning strike is from you is this:

Count the number of seconds between when you see the lightning and hear the thunder. Divide the number of seconds by five to find out how many miles away the lightning hit.

According to this rule, what is the speed of sound in air? How does the speed of sound implied by this rule compare to 340 m/s?

Identify important physics concept :   This question is about speed of sound.

List known and unknown quantities (with letter names and units):

At first glance, it doesn’t look like there’s enough information to solve the problem. We were asked to find speed, but not given either a time or a distance. However, the problem does allow us to figure out a distance if we know the time- “Divide the number of seconds by five to find out how many miles away the lightning hit.” So, let’s make up a time and see what happens; if the time is 10 seconds, the rule of thumb says that the distance should be 2 miles.

[latex]v= \: ?[/latex]

[latex]d=2 \: miles[/latex]

[latex]t=10 \: seconds[/latex]

You might ask “Is making stuff up OK here?” The answer is YES! If the rule of thumb is right, it should work no matter what time we choose. (To check if the rule is OK, we should probably test it with more than just one distance-time combination, but we’ll assume the rule is OK for now).

Do the algebra:  The equation is already solved for speed. Move on to the next step.

Do unit conversions (if needed) then plug in numbers:  If you just plug in the numbers, the speed comes out in miles per second:

[latex]v = \frac{2 \: miles} {10 \: seconds}=0.2 \: \frac{miles} {second}[/latex]

We are asked to compare this speed to 340 m/s, so a unit conversion is in order; since there are 1609 meters in a mile:

[latex]v =0.2 \: \frac{miles} {second}*\frac{1609 \: meters} {1 \:mile}=320 \frac{m}{s}[/latex]

Reflect on the answer:

• The answer for speed from the rule of thumb is less than 10% off the actual value of roughly 340 m/s- surprisingly close!
• At the beginning, we assumed a time of 10 seconds. Does the result hold up for other choices? A quick check shows that it does! For instance, if we use a time of 5 seconds, the rule of thumb gives a distance of 1 mile, and the math still gives a speed of 0.2 miles/second. The speed will be the same no matter what time we pick. The reason is this:  The more time it takes the thunder to arrive, the farther away the lightning strike is, but the speed remains the same. In the equation for speed, both time and distance change by the same factor and the overall fraction remains unchanged.

Stop to think answers

• Both sounds take the same amount of time. (High and low pitched sounds travel at the same speed).
• Both sounds take the same amount of time. (Quiet sounds and loud sounds travel at the same speed).
• The sound of the whale travels the distance in less time- assuming sound from the whale travels in water and sound from the human travels in air. Sound travels faster in water than in air. (The info about frequency was given just to throw you off- frequency doesn’t matter).
• Wolfe, J. (2014, February 20). Properties of Sound. Retrieved from https://www.youtube.com/watch?v=P8-govgAffY ↵

Understanding Sound Copyright © by dsa2gamba and abbottds is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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17.2 Speed of Sound

Learning objectives.

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

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

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display ( Figure 17.4 ). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

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

where v is the speed of the wave, f is its frequency, and λ λ is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions ( Figure 17.5 ). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table 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. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property , divided by the inertial property ,

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

Recall from Waves that the speed of a wave on a string is equal to v = F T μ , v = F T μ , where the restoring force is the tension in the string F T F T and the linear density μ μ is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

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

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

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

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

where the temperature in the first equation (denoted as T C T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas, v rms = 3 k B T m , v rms = 3 k B T m , where k B k B is the Boltzmann constant ( 1.38 × 10 −23 J/K ) ( 1.38 × 10 −23 J/K ) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas v rms v rms describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0 °C 0 °C , the speed of sound is 331 m/s, whereas at 20.0 °C 20.0 °C , it is 343 m/s, less than a 4 % 4 % increase. Figure 17.6 shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics .

Consider fluid flow through a pipe with cross-sectional area A ( Figure 17.7 ). The mass in a small volume of length x of the pipe is equal to the density times the volume, or m = ρ V = ρ A x . m = ρ V = ρ A x . The mass flow rate is

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume, ρ in A in v in = ρ out A out v out . ρ in A in v in = ρ out A out v out .

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries ( Figure 17.8 ). The density, temperature, and velocity on one side of the volume of the fluid are given as ρ , T , v , ρ , T , v , and on the other side are ρ + d ρ , T + d T , v + d v . ρ + d ρ , T + d T , v + d v .

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

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

The net force on the volume of fluid ( Figure 17.9 ) equals the sum of the forces on the left face and the right face:

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = ρ V = ρ d x d y d z . m = ρ V = ρ d x d y d z . We have

From the continuity equation ρ d v = − v d ρ ρ d v = − v d ρ , we obtain

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

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

Here M is the molar mass of air:

Since the speed of sound is equal to v = d p d ρ v = d p d ρ , the speed is equal to

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, γ = 1.4 , γ = 1.4 , M = 0.02897 kg mol , M = 0.02897 kg mol , and R = 8.31 J mol · K . R = 8.31 J mol · K . If the temperature is T C = 20 ° C ( T = 293 K ) , T C = 20 ° C ( T = 293 K ) , the speed of sound is v = 343 m/s . v = 343 m/s .

The equation for the speed of sound in air v = γ R T M v = γ R T M can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

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

In a given medium under fixed conditions, v is constant, so there is a relationship between f and λ ; λ ; the higher the frequency, the smaller the wavelength ( Figure 17.10 ).

Example 17.1

Calculating wavelengths.

• Identify knowns. The value for v is given by v = ( 331 m/s ) T 273 K . v = ( 331 m/s ) T 273 K .
• Convert the temperature into kelvins and then enter the temperature into the equation v = ( 331 m/s ) 303 K 273 K = 348.7 m/s . v = ( 331 m/s ) 303 K 273 K = 348.7 m/s .
• Solve the relationship between speed and wavelength for λ : λ = v f . λ = v f .
• Enter the speed and the minimum frequency to give the maximum wavelength: λ max = ​ 348.7 m/s 20 Hz = 17 m . λ max = ​ 348.7 m/s 20 Hz = 17 m .
• Enter the speed and the maximum frequency to give the minimum wavelength: λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm . λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm .

Significance

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 λ λ must change. That is, because v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.

Check Your Understanding 17.1

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

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves , which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced ( Figure 17.11 ).

Seismologists and geophysicists use properties and velocities of earthquake waves to study the Earth's interior, which due to it's depth and pressure is not observable through many other means. In fact, the discoveries of the structure of the Earth, illustrated in the figure above, resulted from earthquake observations. In 1914, Beno Gutenberg used differences in wave speeds to determine that there must be a liquid core within the mantle. In 1936, Inge Lehmann began investigating P-waves from a New Zealand earthquake that had unexpectedly reached Europe, which should have been in the shadow region. Up until that point, seismologists had explained such shadow waves as being caused by some type of diffraction (as Gutenberg himself assumed) or a result of faulty seismometers. However, Lehmann had installed the European instruments herself, and so trusted their accuracy. She calculated that the amplitude of the waves must be caused by the existence of a solid inner core within the liquid core. This model has been accepted and reinforced by decades of subsequent calculations, including those from nuclear test explosions, which can be measured very precisely.

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

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• TN Navbharat
• Times Drive
• ET Now Swadesh

technology science

Why Does Sound Travel Faster In Solids? Explained

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The speed at which sound travels varies significantly depending on the material it moves through. (Image: Unsplash)

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Sound Waves: Explanation, Review, and Examples

• The Albert Team
• Last Updated On: September 12, 2023

Sound waves fill our world, from music to spoken words to the rustling of leaves in the wind. In this post, we’ll explore what sound waves are, their characteristics like amplitude and frequency, and review the speed of sound. Our aim is to make understanding sound waves straightforward and relatable. So whether you’re curious about how we perceive sound or want to understand the science behind it, this post has got you covered.

What We Review

What Type of Wave is a Sound Wave?

To understand sound, it’s important to know what kind of wave it is. Sound is a longitudinal wave. This means that the particles in the medium (like air) move back and forth in the same direction that the sound wave is traveling. Now let’s break down what this means and why it matters.

Transverse and Longitudinal Waves

Waves can generally be categorized into two types: transverse and longitudinal.

• Transverse Waves: In a transverse wave, the movement of the particles in the medium (could be air, water, etc.) is at right angles to the direction of the wave. Think of a rope being whipped up and down; the wave moves along the length of the rope, but the rope’s actual movement is up and down, perpendicular to the wave direction.
• Longitudinal Waves: In a longitudinal wave, particles in the medium move back and forth along the same line that the wave travels. Imagine pushing and pulling a spring; the compressions and rarefactions (tightening and loosening of the spring’s coils) move along the length of the spring, the same direction in which you pushed or pulled it.

For a full review of transverse and longitudinal waves, be sure to visit our blog post on that topic.

How Sound Waves Are Produced

Sound waves are generated when something vibrates, like a drum skin when struck or vocal cords when you speak. These vibrations push and pull on the air molecules near them, causing these molecules to vibrate back and forth.

How Sound Waves Travel

Sound, being a longitudinal wave, makes the air molecules move in the same direction as the wave itself. For example, when a drum is hit, the drum’s surface vibrates, causing the nearby air molecules to move back and forth along the line of the wave. This series of compressions (where the air molecules are close together) and rarefactions (where they are spread apart) continue to travel through the air as a sound wave. This is how sound gets from the source (like the drum) to your ears.

Knowing that sound is a longitudinal wave helps you understand how it moves from its source, like a speaker, to your ears. This basic idea is key to understanding more detailed aspects of sound, such as its speed, loudness, and pitch.

Aspects of Sound Waves

Now that we understand sound as a longitudinal wave, we can look at the key features that shape how it behaves. These essential aspects are frequency, amplitude, and speed of sound. If you need to review these basic wave characteristics, visit this post to break down mechanical waves.

Frequency of Sound

Frequency refers to how many times a wave oscillates, or cycles, per second. In terms of sound, frequency determines the pitch of the sound you hear. High-frequency sound waves produce high-pitched noises, like a whistle, while low-frequency sound waves produce low-pitched noises, like a drumbeat. Frequency is measured in hertz (Hz), and in everyday life, human hearing ranges from about 20\text{ Hz} to 20{,}000\text{ Hz} .

Amplitude of Sound

Amplitude is another critical aspect of sound. It describes how “tall” the wave is and is directly related to the loudness of the sound. A sound wave with a higher amplitude will be louder than a sound wave with a lower amplitude. Think of amplitude like the volume knob on your stereo; turning it up increases the amplitude of the sound waves, making the sound louder. Amplitude is typically measured in decibels (dB). The table below shows the sound level in decibels for a range of sources.

Speed of Sound

Lastly, let’s talk about the speed of sound, which varies depending on the medium through which it travels. In dry air at room temperature, the speed of sound is approximately 343\text{ meters per second} . In water, it’s faster—about 1{,}500\text{ meters per second} . The speed of sound is affected by factors like temperature, pressure, and the properties of the medium it’s traveling through.

The table below shows the speed of sound in various media. 

By understanding these aspects—frequency, amplitude, and speed—you’ll have a comprehensive view of what sound waves are and how they function. This foundational knowledge sets the stage for a deeper understanding of sound and its many applications in our daily lives.

Technological Applications of Sound Waves

Sound waves have a range of applications in technology, enhancing various aspects of our lives. From musical instruments to medical imaging, the applications are diverse.

Instruments and Music

Musical instruments like guitars, flutes, and drums are classic examples of how sound waves can be manipulated to create harmony and melody. When you pluck a guitar string or hit a drum skin, you’re generating sound waves with specific frequencies and amplitudes. These waves interact to produce the musical tones we enjoy. Understanding the physics behind sound waves helps in the design and optimization of musical instruments, leading to better sound quality and a wider range of tonal possibilities.

Infrasound refers to sound waves with frequencies below the human hearing range, typically less than 20 Hz. Despite being inaudible, these low-frequency waves have several practical applications. They are used in seismology to detect earthquakes and volcanic activity. Infrasound is also used for long-distance communication in certain animal species, such as elephants and whales. Additionally, it has applications in weather forecasting, as some weather phenomena generate infrasonic signals.

Ultrasonic technology

On the opposite end of the spectrum, we have ultrasonic sound waves, which have frequencies higher than the audible range, generally above 20{,}000\text{ Hz} . One of the most well-known applications of ultrasonic waves is in medical imaging, particularly in sonograms and ultrasound scans. These high-frequency waves can penetrate tissues and provide detailed images, making them invaluable in medical diagnostics. Ultrasonic waves are also used in industrial settings for detecting flaws in materials and in distance-measuring devices like sonar.

Understanding how sound waves function across different applications not only broadens our appreciation of their versatility but also opens the door for further technological advancements.

In this post, we’ve taken a comprehensive look at sound waves, starting with the basics of what type of wave sound is—a longitudinal wave. We discussed its key aspects like frequency, amplitude, and speed in various media, breaking down how these properties shape our auditory experiences. Then, we explored the practical applications of sound waves in technology, focusing on musical instruments, infrasound, and ultrasonics. Whether you’re interested in how we hear everyday sounds or in the broader technological applications, understanding these fundamentals provides a solid foundation for further exploration into the world of sound. 

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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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June 27, 2019

What Do You Hear Underwater?

A submerged science activity from Science Buddies

By Science Buddies & Sabine De Brabandere

Make waves--underwater! Learn how sound travels differently in water than it does in the air. 

George Retseck

Key Concepts Physics Sound Waves Biology

Introduction Have you ever listened to noises underwater? Sound travels differently in the water than it does in the air. To learn more, try making your own underwater noises—and listening carefully. 

Background Sound is a wave created by vibrations. These vibrations create areas of more and less densely packed particles. So sound needs a medium to travel, such as air, water—or even solids. 

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Sound waves travel faster in denser substances because neighboring particles will more easily bump into one another. Take water, for example. There are about 800 times more particles in a bottle of water than there are in the same bottle filled with air. Thus sound waves travel much faster in water than they do in air. In freshwater at room temperature, for example, sound travels about 4.3 times faster than it does in air at the same temperature.

Sound traveling through air soon becomes less loud as you get farther from the source. This is because the waves’ energy quickly gets lost along the way. Sound keeps its energy longer when traveling through water because the particles can carry the sound waves better. In the ocean, for example, the sound of a humpback whale can travel thousands of miles!

Underwater sound waves reaching us at a faster pace and keeping their intensity longer seem like they should make us perceive those sounds as louder when we are also underwater. The human ear, however, evolved to hear sound in the air and is not as useful when submerged in water. Our head itself is full of tissues that contain water and can transmit sound waves when we are underwater. When this happens, the vibrations bypass the eardrum, the part of the ear that evolved to pick up sound waves in the air. 

Sound also interacts with boundaries between two different mediums, such as the surface of water. This boundary between water and air, for example, reflects almost all sounds back into the water. How will all these dynamics influence how we perceive underwater sounds? Try the activity to find out! 

Bathtub or swimming pool (a very large bucket can work, too)

Two stainless steel utensils (for example, spoons or tongs)

Two plastic utensils

Small ball 

Adult helper

An area that can get wet (if not performing the activity at a pool)

Floor cloth to cleanup spills (if not performing the activity at a pool)

Other materials to make underwater sounds (optional)

Access to a swimming pool (optional)

Internet access (optional)

Preparation

Fill the bathtub with lukewarm water—or head to the pool—and bring your helper and other materials.

Ask your helper to click one stainless steel utensil against another. Listen. How would you describe the sound? 

In a moment, your helper will click one utensil against the other underwater . Do you think you will hear the same sound? 

Ask your helper to click one utensil against the other underwater. Listen. Does the sound appear to be louder or softer? Is what you hear different in other ways, too?

Submerge one ear in the water. Ask your helper to click one utensil against the other underwater. Listen. How would you describe this sound? 

Ask your helper to click one utensil against the other underwater soon after you submerge your head. Take a deep breath, close your eyes and submerge your head completely or as much as you feel comfortable doing. Listen while you hold your breath underwater (come up for air when you need to!). Does the sound appear to be louder or softer? Does it appear to be different in other ways? 

Repeat this sequence but have your helper use two plastic utensils banging against each other instead.

Repeat the sequence again, but this time listen to a small ball being dropped into the water. Does the sound of a ball falling into the water change when you listen above or below water? Does your perception of this sound change? Why would this happen? 

Switch roles. Have your helper listen while you make the sounds. 

Discuss the findings you gathered. Do patterns appear? Can you conclude something about how humans perceive sounds when submerged in water? 

Extra : Test with more types of sounds: soft as well as loud sounds, high- as well as low-pitched sounds. Can you find more patterns?

Extra: To investigate what picks up the sound wave when you are submerged, use your fingers to close your ears or use earbuds when submerging your head. How does the sound change when you close off your ear canal underwater? Does the same happen when you close off your ear canal when you are above water? If not, why would this be different? 

Extra: Go to the swimming pool and listen to the sound of someone jumping into the water. Compare your perception of the sound when you are submerged with when your head is above the water. How does your perception change? Close your eyes. Can you tell where the person jumped into the water when submerged? Can you tell when you have your head above the water?

Extra: Research ocean sounds and how sounds caused by human activity impact aquatic animals.  

Observations and Results Was the sound softer when it was created underwater and you listened above the water? Did it sound muffled when you had only your ear submerged? Was it fuller when you had your head submerged? 

Sound travels faster in water compared with air because water particles are packed in more densely. Thus, the energy the sound waves carry is transported faster. This should make the sound appear louder. You probably perceived it as softer when you were not submerged, however, because the water surface is almost like a mirror for the sound you created. The sound most likely almost completely reflected back into the water as soon as it reached the surface. 

When you submerged only your ear, the sound probably still appeared muffled. This happens because the human ear is not good at picking up sound in water—after all, it evolved to pick up sound in air. 

When you submerged your head, the sound probably sounded fuller. That is because our head contains a lot of water, which allows the tissue to pick up underwater sound—without relying on the eardrum. It also explains why closing your ear canal makes almost no difference in the sound you pick up while you are underwater. 

If you tried to detect where the sound came from when submerged, you probably had a hard time. Our brain uses the difference in loudness and timing of the sound detected by each ear as a clue to infer where the sound came from. Because sound travels faster underwater and because you pick up sound with your entire head when you are submerged, your brain loses the cues that normally help you determine where the sound is coming from. 

More to Explore Discovery of Sound in the Sea , from the University of Rhode Island and the Inner Space Center Can You Hear Sounds in Outer Space? , from Science Buddies Talk through a String Telephone , from Scientific American Sound Localization , from Science Buddies  Ears: Do Their Design, Size and Shape Matter? , from Scientific American STEM Activities for Kids , from Science Buddies 

This activity brought to you in partnership with Science Buddies

Temperature and the Speed of Sound

After reading this section you will be able to do the following:.

• Observe the demonstrations below and explain the differences in the speed of sound when the temperature is changed.

Temperature and the speed of sound

Temperature is also a condition that affects the speed of sound. Heat, like sound, is a form of kinetic energy. Molecules at higher temperatures have more energy, thus they can vibrate faster. Since the molecules vibrate faster, sound waves can travel more quickly. The speed of sound in room temperature air is 346 meters per second. This is faster than 331 meters per second, which is the speed of sound in air at freezing temperatures.

The formula to find the speed of sound in air is as follows:

v = 331 m / s + 0.6 m / s C × T v=331m/s+0.6 \frac{m/s}{C}\times T

v is the speed of sound and T is the temperature of the air. One thing to keep in mind is that this formula finds the average speed of sound for any given temperature. The speed of sound is also affected by other factors such as humidity and air pressure.

Air Density and Temperature

Suppose that two volumes of a substance such as air have different densities. We know the more dense substance must have more mass per volume. More molecules are squeezed into the same volume, therefore, the molecules are closer together and their bonds are stronger (think tight springs). Since sound is more easily transmitted between particles with strong bonds (tight springs), sound travels faster through denser air.

However, you may have noticed from the table above that sound travels faster in the warmer 40 ∘ ^{\circ} C air than in the cooler 20 ∘ ^{\circ} C air. This doesn't seem right because the cooler air is more dense. However, in gases, an increase in temperature causes the molecules to move faster and this account for the increase in the speed of sound. This will be discussed in more detail on the next page.

• The speed of sound is faster when temperatures are higher.

How do sound waves work?

Sound waves are vibrations that can move us, hurt us, and maybe even heal us.

By Brian S. Hawkins | Updated Jun 1, 2023 2:00 PM EDT

We live our entire lives surrounded by them. They slam into us constantly at more than 700 miles per hour, sometimes hurting, sometimes soothing . They have the power to communicate ideas, evoke fond memories, start fights, entertain an audience, scare the heck out of us, or help us fall in love. They can trigger a range of emotions and they even cause physical damage. This reads like something out of science fiction , but what we’re talking about is very much real and already part of our day-to-day lives. They’re sound waves. So, what are sound waves and how do they work?

If you’re not in the industry of audio, you probably don’t think too much about the mechanics of sound. Sure, most people care about how sounds make them feel, but they aren’t as concerned with how the sound actually affects them. Understanding how sound works does have a number of practical applications , however, and you don’t have to be a physicist or engineer to explore this fascinating subject. Here’s a primer on the science of sound to help get you started.

What’s in a wave

When energy moves through a substance such as water or air, it makes a wave. There are two kinds of waves: longitudinal ones and transverse ones. Transverse waves, as NASA notes , are probably what most people think of when they picture waves—like the up-down ripples of a battle rope used to work out. Longitudinal waves are also known as compression waves, and that’s what sound waves are. There’s no perpendicular motion to these, rather, the wave moves in the same direction as the disturbance.

How sound waves work

Sound waves are a type of energy that’s released when an object vibrates. Those acoustic waves travel from their source through air or another medium, and when they come into contact with our eardrums, our brains translate the pressure waves into words, music, or signals we can understand. These pulses help you place where things are in your environment.

We can experience sound waves in ways that are more physical, not just physiological, too. If sound waves reach  a microphone —whether it’s a plug-n-play  USB livestream mic  or a studio-quality  microphone for vocals —it transforms them into electronic impulses that are turned back into sound by vibrating speakers . Whether listening at home or at a concert, we can feel the deep bass in our chest. Opera singers can use them to shatter glass. It’s even possible to see sound waves sent through a medium like sand, which leaves behind a kind of sonic footprint. 

That shape is rolling peaks and valleys, the signature of a sine (aka sinusoid) wave. If the wave travels faster, those peaks and valleys form closer together. If it moves slower, they spread out. It’s not a poor analogy to think of them somewhat like waves in the ocean. It’s this movement that allows sound waves to do so many other things. 

It’s all about frequency

When we talk about a sound wave’s speed, we’re referring to how fast these longitudinal waves move from peak to trough and back to peak. Up … and then down … and then up … and then down. The technical term is frequency , but many of us know it as pitch. We measure sound frequency in hertz (Hz), which represents cycles-per-second, with faster frequencies creating higher-pitched sounds. For instance, the A note right above Middle C on a piano is measured at 440 Hz—it travels up and down at 440 cycles per second. Middle C itself is 261.63 Hz—a lower pitch, vibrating at a slower frequency.

Understanding frequencies can be useful in many ways. You can precisely tune an instrument by analyzing the frequencies of its strings. Recording engineers use their understanding of frequency ranges to dial in equalization settings that help sculpt the sound of the music they’re mixing . Car designers work with frequencies—and materials that can block them—to help make engines quieter. And  active noise cancellation  uses artificial intelligence and algorithms to measure external frequencies and generate inverse waves to cancel environmental rumble and hum, allowing top-tier ANC headphones and earphones to isolate the wearer from the noise around them. The average frequency range of human hearing is 20 to 20,000 Hz.

What’s in a name? 

The hertz measurement is named for the German physicist Heinrich Rudolf Hertz , who proved the existence of electromagnetic waves. 

Getting amped

Amplitude equates to sound’s volume or intensity. Using our ocean analogy—because, hey, it works—amplitude describes the height of the waves.

We measure amplitude in decibels (dB). The dB scale is logarithmic, which means there’s a fixed ratio between measurement units. And what does that mean? Let’s say you have a dial on your guitar amp with evenly spaced steps on it numbered one through five. If the knob is following a logarithmic scale, the volume won’t increase evenly as you turn the dial from marker to marker. If the ratio is 4, let’s say, then turning the dial from the first to the second marker increases the sound by 4 dB. But going from the second to the third marker increases it by 16 dB. Turn the dial again and your amp becomes 64 dB louder. Turn it once more, and you’ll blast out a blistering 256 dB—more than loud enough to rupture your eardrums. But if you’re somehow still standing, you can turn that knob one more time to increase your volume to a brain-walloping 1,024 decibels. That’s almost 10 times louder than any rock concert you’ll ever encounter, and it will definitely get you kicked out of your rehearsal space. All of which is why real amps aren’t designed that way.

Twice as nice

We interpret a 10 dB increase in amplitude as a doubling of volume. 

Parts of a sound wave

Timbre and envelope are two characteristics of sound waves that help determine why, say, two instruments can play the same chords but sound nothing alike. 

Timbre is determined by the unique harmonics formed by the combination of notes in a chord. The A in an A chord is only its fundamental note—you also have overtones and undertones. The way these sound together helps keep a piano from sounding like a guitar, or an angry grizzly bear from sounding like a rumbling tractor engine. 

[Related: Even plants pick up on good vibes ]

But we also rely on envelopes, which determine how a sound’s amplitude changes over time. A cello’s note might swell slowly to its maximum volume, then hold for a bit before gently fading out again. On the other hand, a slamming door delivers a quick, sharp, loud sound that cuts off almost instantly. Envelopes comprise four parts: Attack, Decay, Sustain, and Release. In fact, they’re more formally known as ADSR Envelopes. 

• Attack: This is how quickly the sound achieves its maximum volume. A barking dog has a very short attack; a rising orchestra has a slower one. 
• Decay: This describes how fast the sound settles into its sustained volume. When a guitar player plucks a string , the note starts off loudly but quickly settles into something quieter before fading out completely. The time it takes to hit that sustained volume is decay. 
• Sustain: Sustain isn’t a measure of time; it’s a measure of amplitude, or volume. It’s how loud the plucked guitar note is after the initial attack but before it fades out. 
• Release: This is the time it takes for the note to drift off to silence. 

Speed of sound

Science fiction movies like it when spaceships explode with giant, rumbling, surround-sound booms . However, sound needs to travel through a medium so, despite Hollywood saying otherwise, you’d never hear an explosion in the vacuum of space. 

Sound’s velocity , or the speed it travels at , differs depending on the density (and even temperature) of the medium it’s moving through—it’s faster in the air than water, for instance. Generally, sound moves at 1,127 feet per second, or 767.54 miles per hour. When jets break the sound barrier , they’re traveling faster than that. And knowing these numbers lets you estimate the distance of a lightning strike by counting the time between the flash and thunder’s boom—if you count to 10, it’s approximately 11,270 feet away, or about a quarter-mile. (Very roughly, of course.) 

A stimulating experience

Anyone can benefit from understanding the fundamentals of sound and what sound waves are. Musicians and content creators with home recording set-ups and studio monitors obviously need a working knowledge of frequencies and amplitude. If you host a podcast, you’ll want as many tools as possible to ensure your voice sounds clear and rich, and this can include understanding the frequencies of your voice, what microphones are best suited to them , and how to set up your room to reflect or dampen the sounds you do or do not want. Having some foundational information is also useful when doing home-improvement projects— when treating a recording workstation , for instance, or just soundproofing a new enclosed deck. And who knows, maybe one day you’ll want to shatter glass. Having a better understanding of the physics of sound opens up wonderful new ways to explore and experience the world around us. Now, go out there and make some noise!

This post has been updated. It was originally published on July 27, 2021.

Brian is a documentary producer, director, and cameraman on feature films and docu-series, and has more than 20 years’ experience as a journalist. He enjoys covering pop-culture, tech, and the conflation of the two.

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How far does sound travel in the ocean?

The distance that sound travels in the ocean varies greatly, depending primarily upon water temperature and pressure..

Water temperature and pressure determine how far sound travels in the ocean.

While sound moves at a much faster speed in the water than in air , the distance that sound waves travel is primarily dependent upon ocean temperature and pressure. While pressure continues to increase as ocean depth increases, the temperature of the ocean only decreases up to a certain point, after which it remains relatively stable. These factors have a curious effect on how (and how far) sound waves travel.

Imagine a whale is swimming through the ocean and calls out to its pod. The whale produces sound waves that move like ripples in the water. As the whale’s sound waves travel through the water, their speed decreases with increasing depth (as the temperature drops), causing the sound waves to refract downward . Once the sound waves reach the bottom of what is known as the thermocline layer, the speed of sound reaches its minimum. The thermocline is a region characterized by rapid change in temperature and pressure which occurs at different depths around the world. Below the thermocline "layer," the temperature remains constant, but pressure continues to increase. This causes the speed of sound to increase and makes the sound waves refract upward .  

The area in the ocean where sound waves refract up and down is known as the "sound channel." The channeling of sound waves allows sound to travel thousands of miles without the signal losing considerable energy.  In fact, hydrophones, or underwater microphones, if placed at the proper depth, can pick up whale songs and manmade noises from many kilometers away.

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More information.

• Noise in the Ocean: A National Issue (National Marine Sanctuaries)
• Just how noisy is the ocean? Learn about a NOAA Effort to Monitor Underwater Sound
• Sound in the Sea Gallery
• Acoustic Monitoring

Last updated: 01/20/23 Author: NOAA How to cite this article