This is a simulation of a standard physics demonstration to measure the speed of sound in air. A vibrating tuning fork is held above a tube - the tube has some water in it, and the level of the water in the tube can be adjusted. This gives a column of air in the tube, between the top of the water and the top of the tube. By setting the water level appropriately, the height of the air column can be such that it gives a resonance condition for the sound wave produced by the tuning fork. In the real experiment, resonance is found by listening - the sound from the tube is loudest at resonance. In the simulation, resonance is shown by the amplitude of the wave in the air column. The larger the amplitude, the closer to resonance. Note that at certain special heights of the air column, no sound is heard - this is because of completely destructive interference.
In addition, there is always a node (for displacement of the air molecules) at the water surface. To a first approximation, resonance occurs when there is an anti-node at the top of the tube. Knowing the frequency of the tuning fork, the height of the air column, and the appropriate equation for standing waves in a tube like this, the speed of sound in air can be determined experimentally. What do you get for the speed of sound in air in this simulation?
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Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is
The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period of time.
Factors Affecting Wave Speed
The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity. (Elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed ( v ) of a wave, thus yielding this general pattern:
Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property . The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. As stated above, sound waves travel faster in solids than they do in liquids than they do in gases. However, within a single phase of matter, the inertial property of density tends to be the property that has a greatest impact upon the speed of sound. A sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium than it will in air. This is mostly due to the lower mass of Helium particles as compared to air particles.
The Speed of Sound in Air
The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor being present in air. Like any liquid, water has a tendency to evaporate. As it does, particles of gaseous water become mixed in the air. This additional matter will affect the mass density of the air (an inertial property). The temperature will affect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:
where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.
v = 331 m/s + (0.6 m/s/C)•(20 C)
v = 331 m/s + 12 m/s
v = 343 m/s
(The above equation relating the speed of a sound wave in air to the temperature provides reasonably accurate speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)
Look It Up!
Using wave speed to determine distances.
At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and the lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of
If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.
Another phenomenon related to the perception of time delays between two events is an echo . A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 1.40 seconds after making the holler , then the distance to the canyon wall can be found as follows:
The canyon wall is 242 meters away. You might have noticed that the time of 0.70 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.
While an echo is of relatively minimal importance to humans, echolocation is an essential trick of the trade for bats. Being a nocturnal creature, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves that reflect off objects in their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses. These bats are utilizing the physics of the Doppler effect discussed in an earlier unit (and also to be discussed later in Lesson 3 ). This method of echolocation enables a bat to navigate and to hunt.
The Wave Equation Revisited
Like any wave, a sound wave has a speed that is mathematically related to the frequency and the wavelength of the wave. As discussed in a previous unit , the mathematical relationship between speed, frequency and wavelength is given by the following equation.
Using the symbols v , λ , and f , the equation can be rewritten as
Check Your Understanding
1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object?
Answer = 25.5 m
The speed of the sound wave is 340 m/s. The distance can be found using d = v • t resulting in an answer of 25.5 m. Use 0.075 seconds for the time since 0.150 seconds refers to the round-trip distance.
2. On a hot summer day, a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second.
a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?
Part a Answer: 600 Hz (given)
Part b Answer: 0.583 meters
3. Doubling the frequency of a wave source doubles the speed of the waves.
a. True b. False
Doubling the frequency will halve the wavelength; speed is unaffected by the alteration in the frequency. The speed of a wave depends upon the properties of the medium.
4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C.
Answer: 1.35 meters (rounded)
Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 256 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.
5. Most people can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to this upper range of audible hearing.
Answer: 0.0173 meters (rounded)
Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 20 000 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.
6. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.
Answer: 34.5 meters
Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 10 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.
7. Determine the speed of sound on a cold winter day (T=3 degrees C).
Answer: 332.8 m/s
The speed of sound in air is dependent upon the temperature of air. The dependence is expressed by the equation:
v = 331 m/s + (0.6 m/s/C) • T
where T is the temperature in Celsius. Substitute and solve.
v = 331 m/s + (0.6 m/s/C) • 3 C v = 331 m/s + 1.8 m/s v = 332.8 m/s
8. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls?
Answer = 209 m
The speed of the sound wave at this temperature is 343 m/s (using the equation described in the Tutorial). The distance can be found using d = v • t resulting in an answer of 343 m. Use 0.61 second for the time since 1.22 seconds refers to the round-trip distance.
9. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The velocity of wave B must be __________ the velocity of wave A.
a. one-ninth b. one-third c. the same as d. three times larger than
The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.
10. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.
Since Wave B has three times the wavelength of Wave A, it must have one-third the frequency. Frequency and wavelength are inversely related.
- Interference and Beats
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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
Related Posts
NOTIFICATIONS
Measuring the speed of sound.
- + Create new collection
In this investigation, students measure distance and time in order to calculate the speed of a sound wave.
The investigation supports the science capability ‘Gather and interpret data’. It also provides a real-world context in which to practise mathematical skills.
By the end of this investigation, students should be able to:
- calculate the speed of sound
- explain why we see a lightning bolt before we hear the thunder.
Equipment required includes:
- sound-making device (wooden clapper)
- device with timing software app
- tape measure
- an outdoor space of at least 150 metres with a building at one end.
Download the Word file (see link below).
Related content
This article is part of an article series :
- Sound – understanding standing waves
- Sound – visualising sound waves
- Sound – resonance
- Sound – wave interference
- Sound – beats, the Doppler effect and sonic booms
with the accompanying investigation:
- Investigating sound wave resonance
Learn more about sound with these articles:
- Hearing sound
- Sound on the move
- Measuring sound
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| A clap echo experiment Here the camera and I were both 30 m from the wall of the building. My hands were 2 m from the camera and its microphone. So sound goes from my clapping hands via two different paths: by reflection from the wall, with a total distance of 60 m, or directly, 2 m. The difference in path is 58 m. --> |
| In this case, we can clearly see the clap and the echo in the sound track. However, I have amplified the echo in the sound track to make it more readily visible in this small screen sample Expanding the time scale, it's easy to measure to a precision of a couple of ms. The chief error is in deciding what features to recognise in the clap and echo. So sound has travelled the extra 58 m in 0.17 s, giving a speed of 340 m/s. |
| Time of flight: light sound Sound is much slower than light: 340 m/s 300,000,000 m/s. Nearly a million times slower. So the image arrives almost instantaneously. Here we compare the image and the sound of the collision of the wood blocks.
--> |
| 115 m takes me most of the way across a cricket field. But we still only have a few hundred ms. And the problem is that the camera only runs at 25 frames per second. Where on the soundtrack is the collision? To locate the collision on the soundtrack, I used the second and third images to estimate the speed of the blocks and used that to position the collision between the second and third frame. This gives a time delay of 0.34 s, and so again a speed of 340 m/s. The interpolation is only one concern in this experiment: we also didn't know how the camera labelled images with times. So the echo experiment above is, we think, more reliable. |
| Two microphones and a long cable The next experiment will use a long cable. Actually we used all the long cables from our lab and from a nearby lab and connected them together to give us a total length of 34 m. We know that coaxial cables both slow the electric signal and attenuate the high frequencies - though of course high frequency here means high frequencies. Can this be detected in the sound? Probably not, but worth demonstrating. So we conneceted one microphone to one channel, and the other microphone via the 34 m cable to the other channel.
--> |
| Not much difference. No surprise. For the original cable under the Atlantic Ocean, however, attenuation and delays were very significant and limited tele speeds to less than a word per minute. |
| Time of flight with a cable --> |
Here we used two microphones, 33.03 m apart. Again, the weaker signal has been amplified to make it easier to see on the soundtrack. The delay is 96 ms, which gives a speed of 340 m/s. |
| Effect of transmission through air? --> |
This experiment was not a convincing one. What we wanted to do was to compare the timbre of sound that had travelled 30 m through air with one that had travelled less that one metre. The left channel travels one metre through air then 30 m through the cable. The right channel signal travels 30 m through the air and 2 m through cables. Again, similar microphones. Because of nonadiabatic losses in transmission, high frequencies are attenuated more than low and, at 30 m, we calculated that one might expect to hear a difference. Provided, of course that the background noise doesn't mask the differences. Briefly, the campus is near the city, has abundant bird-life and is near to the coast so that wind is rarely less than a few knots. By the time that we'd lay out a cable, students or gardeners would appear.... Okay, if you know a really quiet, open location and can lay your hands on several tens of metres of coaxial cable and two microphones, we'd like to hear from you! |
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17.2 Speed of SoundLearning objectives. By the end of this section, you will be able to:
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 MediaTable 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 AirAs 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 17.1Calculating wavelengths.
SignificanceThe 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 17.1Imagine 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. This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax. Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
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To Find the Speed of Sound in Air at Room Temperature Using a Resonance Tube by Two Resonance PositionsTo find the speed of sound in air at room temperature using a resonance tube by two resonance positions. Apparatus/Materials Required
 Let l 1 and l 2 be the length of the air column for the first and second resonance respectively with a tuning fork of frequency f . The speed is given by the formula Substituting, we get
ObservationThe temperature of the air in the air column: (i) in the beginning ____ °C (ii) at the end _____°C The mean temperature is calculated as follows: Frequency of first tuning fork = f 1 Frequency of second tuning fork = f 2
CalculationFrom the first tuning fork, From the second tuning fork, The mean velocity at room temperature is given as follows: At room temperature, the velocity of sound in air is _____ m/s. 1. What is the working principle of the resonance tube? It works on the principle of resonance of the air column with a tuning fork. 2. What types of waves are produced in the air column? Longitudinal stationary waves are produced in the air column. 3. Do you find the velocity of sound in air column or in the water column? The velocity of sound is found in the air column above the water column. 4. What are the possible errors in the result? The two possible errors in the result are: (i) The enclosed air in the air column is denser than the outside air, this may reduce the velocity of air. (ii) The humidity above the enclosed water column may increase the velocity of sound. 5. Will the result be affected if we take other liquids than water? No, it will not be affected. Sound Visualisation Stay tuned with BYJU’S to get the latest notification on CBSE along with CBSE syllabus, sample papers, marking scheme and more.
 Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin! Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz Visit BYJU’S for all Physics related queries and study materials Your result is as below Request OTP on Voice Call
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IMAGES
VIDEO
COMMENTS
Measuring the speed of sound. This is a simulation of a standard physics demonstration to measure the speed of sound in air. A vibrating tuning fork is held above a tube - the tube has some water in it, and the level of the water in the tube can be adjusted. This gives a column of air in the tube, between the top of the water and the top of the ...
At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation: v = 331 m/s + (0.6 m/s/C)•T. 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 ...
A sound wave is a mechanical vibration that propagates through a medium, such as air or a liquid. The speed of sound is the speed at which this wave propagates in this m edium, it depends on the temperature, the pressure and the density of the medium through which it propagates. In air, if we assimilate it to a perfect diatomic gas, we can calculate the speed of sound by the equation: c = sqrt ...
A common experiment in physics education is to measure the speed of sound c in air, or other gasses, by observing standing acoustic waves in a tube. August Kundt first described this experiment in 1866 . Such an experiment is therefore often referred to as Kundt's tube.
Learn how to calculate the speed of sound in different materials and factors that affect it. Find out the speed of sound on Mars and the hot chocolate effect.
Learn how to measure the speed of sound in air using a tuning fork and a sound tube. Follow the procedure, calculate the wavelength and the speed of sound, and compare with the theoretical value.
Physics 2310 Lab #2 Speed of Sound & Resonance in Air. Objective: The objectives of this experiment are a) to measure the speed of sound in air, and b) investigate resonance within air. Figure 1: The experimental setup for measuring the speed of sound. Figure 2: The oscilloscope and function generator.
Compared to most things you study in the physics lab, sound waves travel very fast. It is fast enough that measuring the speed of sound is a technical challenge. One method you could use would be to time an echo. For example, if you were in an open field with a large building a quarter of a kilometer away, you could start a stopwatch when a loud noise was made and stop it when you heard the ...
This video shows how we can measure the speed of sound in air. In order to calculate the speed of a wave, we need to measure the distance covered by a wave i...
The amplitude of a sound wave decreases with distance from its source, because the energy of the wave is spread over a larger and larger area. But some of the energy is also absorbed by objects, such as the eardrum in Figure 14.5, and some of the energy is converted to thermal energy in the air. Figure 14.4 shows a graph of gauge pressure versus distance from the vibrating string.
Measuring the speed of sound. In this investigation, students measure distance and time in order to calculate the speed of a sound wave. The investigation supports the science capability 'Gather and interpret data'. It also provides a real-world context in which to practise mathematical skills. By the end of this investigation, students ...
So sound has travelled the extra 58 m in 0.17 s, giving a speed of 340 m/s. Time of flight: light vs sound Sound is much slower than light: 340 m/s vs 300,000,000 m/s.
English as a Second Language (Speaking Endorsement) Past Papers. Edexcel. English Language A. Paper 1 (Non-fiction Texts and Transactional Writing) Paper 2 (Poetry and Prose Texts and Imaginative Writing) Paper 3 (Coursework) English Language B.
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.
Fix the reservoir R in the uppermost position. Loosen the pinch cock P and fill the reservoir and metallic tube completely with water by a beaker. Tighten the pinch cock, lower the reservoir and fix it in the lowest position. Take a tuning fork of higher frequency.
Strike the tuning fork with the rubber hammer and hold above the top of the tube. 5. Adjust the height of the tube until the sound is loudest. Hold the tube still and measure and record the distance from the water to the top of the tube. 6. Hold a thermometer in the middle of the tube and record the air temperature. Part B. 1.
The goal of this activity is for students to devise an experiment that allows them to determine the speed of sound through air. In the Preliminary Observations, students will observe sound waves that are "delayed" in their arrival, such as seeing a gun flash before hearing it. Students will then estimate how fast sound waves travel through air and devise a method for measuring it. Since groups ...
9. Calculate the average speed of sound for a given frequency using the speeds of sound calculated in the previous step. Also determine the standard deviations. Finally, compare the average speeds of sound from part B to the speed of sound determined in part A of the experiment. Data
We recommend using the latest version of Chrome, Firefox, Safari, or Edge. This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears.