- Feb 2, 2023
Seven experiments to measure the speed of sound in the air
Updated: Feb 15
Calculating the speed of sound becomes a simple and engaging task with the use of a smartphone, transforming this commonly abstract concept into a tangible learning experience. For students, this exercise is particularly gratifying as it demystifies the complexities of sound waves, allowing them to explore its various physical properties through a device that's a familiar staple in their everyday lives. In this article, we introduce seven experiments, each utilizing a smartphone and the FizziQ app , to determine the speed of sound, making science interactive and accessible.
Sound waves and their propagation - Methods for measuring the speed of sound - Measurement by time of flight - Measurement by wavelength - Measurement by resonance frequency - Conclusion
Sound waves and their propagation
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(γ*RT/Ma), c, the speed of sound, γ, the ratio of heat capacities at constant pressure and volume. γ= 7/5 for air, R, the ideal gas constant, T, the absolute temperature of the medium, Ma, the molar mass of air: Ma = 29g/mol. Using the previous formula we can calculate the theoretical speed of sound at the usual conditions of temperature and pressure: c = 343 m/s for a temperature of 20 degrees, or approximately 767 miles per hour. In water, sound travels more than 4 times faster than in air, i.e. at about 1,482 meters per second, and in some metals like soft iron, it travels significantly faster at close to 6,000 m/s (13,333 miles per hour).
How to measure the speed of sound with a smartphone?
There are many different ways to measure the speed of sound using a smartphone or a tablet. These methods fall into three broad categories, which, interestingly, use different physical characteristics of sound waves :
Estimating the time of flight (ToF )
Measuring the sound frequency using an Helmholtz resonator
Measuring the wavelength at a given frequency
These are the methods that have been used by generations of scientists to determine the speed of sound:
➡️ Marin Mersenne, the first, evaluated in 1635 the speed of sound in air at 448 m/s by the propagation time method. Value further refined by the scientists Viviani and Borelli in 1656 with a value of 344 m/s.
➡️ Isaac Newton took a different approach through an analytical method by determining it from the resonant frequencies of sound waves in a U-tube and details his method in the first edition ofIt begins (1687).
➡️ Over the centuries, as estimations were more accurate, one uncertainty remained: could humans go faster than the speed of sound? This question will be resolved in 1947 when American aviator Chuck Yeager reached Mach 1 aboard the X-1 aircraft . Once again, the human had crossed an impassable barrier.
Now, the iconic measurement of the speed of sound is readily accessible to anyone. You can delve into these experiments using one or more smartphones, with no need for specialized equipment. Embark on a journey of discovery right at your fingertips, grab your cellphones and let's dive into this exciting venture!
Measuring the Time of Flight (ToF)
Like any speed calculation, the objective here is to determine the time it takes for a sound wave to travel a certain distance . The speed of sound being high, the measurement of time requires a specific equipment: an acoustic stopwatch.
An acoustic stopwatch measures the time difference between two sounds which sound level exceeds a certain threshold. This device cannot be found on a lab bench but many smartphone applications exist that offer this functionality. In FizziQ, you will find the acoustic stopwatch in the Tools menu. You can also build your own acoustic stopwatch using triggers .
The traditional protocol for measuring the speed of sound with an acoustic stopwatch is as follows: two smartphones are separated by a certain distance (at least 5 meters), and an operator is placed near each telephone. The operators clap their hands one after the other. The first clap starts both stopwatch and the seconds stops them. Students then check that the time difference dt between the two stopwatches is dt = 2*d/c, where d is the distance between the smartphones, c the speed of sound. This experiment allows an accuracy between 5 and 10%, and can be improved by performing several measurements. An opportunity to do a bit of statistics as well !
The protocol works well, but younger students find it often difficult to understand the offset formula calculation which is not very intuitive. We prefer a variation of this protocol developed by Aline Chaillou of the La main à la pâte Foundation.
In this second protocol, we start by synchronizing the chronometers by putting them side by side and trigger the sound chronometers by clapping our hands. Then, we move one of the two smartphone by a certain distance d without making noise. An operator located near this second laptop then stops the two stopwatches by clapping his hands. The calculation of the shift is then very intuitive for the students because they have immediately put in relation the difference in distance which creates the phase shift with the displacement of one of the two smartphones.
The time difference dt is equal to: dt = d/c.
This second protocol also makes it possible to introduce the notion of clock synchronization. It is the same concept of synchronization that was used in the famous Hafele-Keating experiment in 1971 to prove relativity. Be mindful to calibrate the trigger level of the sound stopwatch so that it does not trigger when you move one of the two smartphones.
Watch our vidéo :
Measuring the speed of sound with Helmholtz resonators
The second method of calculating the speed of sound is based on the principle of acoustic resonance, which is a phenomenon in which an acoustic system amplifies sound waves whose frequency corresponds to one of its own frequencies of vibration. The resonance frequencies of certain cavities like a cylinders or a bottles are easy to determine by calculus. This frequency depends on the speed of sound and the shape of the object. By measuring the resonance frequency we can infer the speed of sound.
A very simple first protocol consists of blowing on the edge of a graduated test tube. This emits a sound for which we can measure the fundamental frequency using FizziQ. For a closed tube, the fundamental resonance frequency is: f₀ = c(4*L+1.6*D), where L is the length of the tube, D is the diameter of the tube.
To make more precise measurements, we can measure the frequency for different heights of water in the test piece, and by doing a linear regression of the results, we can accurately determine the speed of sound to less than one percent.
If you are a Bordeaux lover and have an empty bottle, you can use a bottle from this region whose volumetric characteristics are immutable. Ulysse Delabre in this video details the calculations for measuring the resonance frequency when blowing into the bottle.
What if the bottle is unopened? It is still possible to carry out the experiment and, paradoxically, in an even simpler way: by uncorking it! When the cork is removed, a "pop" is heard which is due to the resonance of the air in the part between the liquid and the top of the bottle. If we measure the frequency of pop with the frequency meter, we can use the previous formula of the resonant frequency of a tube to deduce the speed of sound.
A last protocol which always surprises students uses the fact that if several frequencies are emitted simultaneously in a cavity, the harmonics of the resonant frequency of the cavity will be amplified compared to the other emitted frequencies. If we measure the spectrum of a white noise emitted in this cavity, the harmonic frequencies of the resonant frequency are highlighted compared to the others. It is recalled that white noise is a random succession of sound emitted in all frequencies. White noise sounds can be found in FizziQ's sound library.
So let's take a tube open at both ends, such as a paper towel roll or a vacuum cleaner hose. At one end of the tube, we will emit a white noise that can be generated with the FizziQ sound library or by using the sound of a video emitting white or pink noise. At the other end of the tube, we measure the frequency spectrum. Measuring the white noise spectrum through a tube will show peaks for the fundamental frequency and its harmonics. We deduce the resonance frequency then the speed of sound by the formula of the resonance frequency of an open tube : f₀ = c(2*L+1.6*D)
Better results are often obtained with pink noise, which is similar to white noise, but with a reduced loudness for high-pitched sounds. The use of pink noise makes it possible to reinforce the intensity of the fundamental resonant frequency compared to its higher harmonics. Examples of of pink noise can be found on internet.
Finally, one can make different measurements with different sizes of the tube, and deduce c by measuring the slope on the graph.
Measuring the speed of sound with waves interferences
This third type of protocol is based on measuring the wavelength of a pure sound of known frequency. We deduce the speed by the relation: c = l.f, with l the wavelength and f the frequency.
This method is the one usually used in the school labs. It uses a sound source and two microphones placed at a certain distance from this source and connected to an oscilloscope with a dual input. By moving the two microphones relative to each other, the operator finds the distance for which the two waves are in phase, which is the wavelength.
With smartphones, this protocol is not possible because they do not have dual sound inputs... However with a little imagination we can find other ways!
The first protocol that we propose consists in using two smartphones that emit the same pure sound, for example at a frequency of 680 hertz. By placing the smartphones at a certain distance, we will calculate the places along the two smartphones axis where waves add up and places where they cance.
With FizziQ one can use the sound at 680 hertz from the sound library. Two smartphones are placed about 3 meters from each other. A third smartphone is used to measure the sound intensity (oscillogram instrument on FizziQ) along the axis of the two smartphones. The interference of the two waves creates zones of very high intensities, the antinodes, and other very weak ones, the nodes. The distance between the nodes (about 50 cm) is equal to the wavelength of the sound wave for the frequency 680 hertz. By measuring the difference between the nodes (or the bellies), we calculate the speed of sound.
This experience also opens an interesting discussion on how active noise reduction headphones work by carrying out a small activity: https://www.fizziq.org/en/team/noise-cancellation
The experiment can also be carried out with only two mobile phones. One of the two smartphones then serves as a transmitter, and also as a tool for measuring the sound volume. A second mobile that emits a pure sound of the same frequency is approached to the first, and the distance between the knot and the belly is noted by measuring the sound volume on the first smartphone, identified by the variations in intensity. To carry out this experiment with FizziQ, we prefer to use the sound intensity measured with the Oscilloscope instrument and which is more precise than the sound volume in decibels.
Finally, if you only have a smartphone, it is also possible to carry out this experiment by placing a reflective surface in place of the second smartphone from the previous experiment. The precision is further reduced but the calculation is nevertheless possible!
These different experiments make it possible to calculate the speed of sound with an accuracy of about 10%.
To conclude
We have identified a number of different ways to estimate the speed of sound. These experiments can be classified into three categories that relate to different physical properties of sound waves. All of these experiments can be done with FizziQ, or with other mobile or tablet apps, depending on your preference. The smartphone is one of the best tools available for measuring the speed of sound, offering multiple ways to approach the same problem, and easily accessible to students. Happy experimenting!
Recent Posts
Seven Experiments on Gravity with your Smartphone
Measuring Pi with Smartphone Sensors: A Fun and Educational Challenge
5 science projects in biomechanics with a smartphone
Talk to our experts
1800-120-456-456
- To Find the Speed of Sound in Air at Room Temperature Using a Resonance Tube By Two Resonance Positions
Resonance in an Air Column
The physics practicals play a crucial role in helping the students understand the concepts better by doing them practically. It offers them hands-on experience of how the phenomenon takes place. We provide the complete experiment, how to conduct it, the substitution of values, and the further procedure that follows. With the resonance experiment Class 11, you can better understand the resonance concepts. We provide these experiments in PDF downloadable form to conduct them easily and quickly while you are at work .
What is Resonance?
Before jumping directly into the experiment, let’s recall what Resonance is.
When a person knocks, strikes, strums, plucks or otherwise disturbs a musical instrument, it is sent into vibrational motion at its inherent frequency. Each object's native frequency corresponds to one of the several standing wave patterns that might cause it to vibrate. The harmonics of a musical instrument are commonly referred to as the instrument's inherent frequencies. If another interconnected item pushes it with one of those frequencies, it can be compelled to vibrate at one of its harmonics (with one of its standing wave patterns). This is known as resonance, which occurs when one thing vibrates at the same natural frequency as another, causing the second object to vibrate.
Resonance Tube
A resonance tube (a hollow cylindrical tube partially filled with water and driven into vibration by a tuning fork) is one of our finest models of resonance in a musical instrument. The tuning fork was the item that induced resonance in the air inside the resonance tube. The tines of the tuning fork vibrate at their natural frequency, causing sound waves to impinge on the resonance tube's aperture. The tuning fork's impinging sound waves cause the air within the resonance tube to vibrate at the same frequency.
In the absence of resonance, however, the sound of these vibrations is inaudible. Only when the first thing vibrates at the inherent frequency of the second object does resonance occur. If the tuning fork vibrates at a frequency that is not the same as one of the natural frequencies of the air column within the resonance tube, resonance will not occur, and the two items will not make a loud sound together. However, by raising and lowering a reservoir of water and therefore decreasing or increasing the length of the air column, the position of the water level may be changed so that the air column vibrates with the same frequency of the tuning fork causing the resonance to occur.
Experiment to Find the Speed of Sound in Air
The aim is to find the speed of sound in air at room temperature using a resonance tube by two resonance positions.
Apparatus Required for Resonance Experiment Physics:
Resonance tube
Two-timing forks having frequencies that are known (for example, 512Hz and 480Hz)
Thermometer
Set squares
Water contained in a beaker
Consider the length of two air columns for first and second resonance as l 1 and l 2 . Let the frequency of the tuning fork be f.
Then, the formula is
\[\lambda = 2\left ( I_{2}- I^{_{1}} \right )\]
The speed of air is calculated using the formula:
\[ v= f\lambda\]
On substituting the value in the formulae, we get,
\[v = 2f\left ( I_{2}- I^{_{1}} \right )\]
The Procedure of the Resonance Tube Experiment:
Make the base horizontal by the levelling screws. Following this, keep the resonance tubes vertical.
Next, in the uppermost position, fix the reservoir R.
Make the pinchcock lose. Fill water from the beaker in the reservoir and metallic tube.
Fix the reservoir in the lowest position, by lowering the reservoir and tightening the pinchcock.
Next, use a tuning fork of higher frequency to experiment.
Vibrate this tuning fork with the help of a rubber pad. Just over the end of the metallic tube, hold the vibrating tongs in a vertical plane.
Next, loosen the pinchcock a bit to allow the water to fall into the metallic tube. When you hear the sound from the metallic tube, lose the pinchcock a bit.
Repeat the above step till you hear the sound with maximum loudness from the metallic tube.
By using the set square, against the meter scale, measure the position of the water level.
Decrease the water level by 1 cm. And then tighten the pinchcock.
Again, repeat the above step till maximum loudness is heard.
After this, repeat the steps with a tuning fork of lower frequency.
Record your observations and put them in the resonance tube formula as given below:
Observations:
The temperature of the air column:
In the beginning:
At the end:
Calculate the mean temperature using the formula:
\[t = \frac{t_{1}+t_{2}}{2}\]
f 1 = frequency of the first tuning fork
f 2 = frequency of the second tuning fork
Calculations:
Observations from the first tuning fork,
\[v_{1} = 2f_{1}(I_{2}'I_{1}'))\]
Observations from the second tuning fork,
\[v_{2} = 2f_{2}(I_{2}”I_{1}”))\]
Calculate the mean velocity using the formula:
\[v = \frac{v_{1}+v_{2}}{2}\]
The speed of air at room temperature is ____ m/s.
Precautions :
Keep the resonance tube vertical.
Ensure that the pinchcock is tight.
Vibrate the tuning fork lightly using the rubber pad.
While vibrating the prongs, ensure that they are vertical at the mouth of the metallic tube.
Carefully read the water level rise and fall.
Use a set square to record the readings.
Sources of Error:
Loose pinchcock.
Resonance tubes might not be uptight.
The air column contains humidity which can lead to an increase in velocity.
1. What is the working principle of the resonance tube?
Answer: The idea of the resonance tube is based on the resonance of an air column with a tuning fork. Transverse stationary waves are formed in the air column. The wave's node is at the water's surface, while the wave's antinode is at the tube's open end.
2. What types of waves are produced in the air column?
Answer: The air column produces longitudinal stationary waves. The standing wave is another name for a stationary wave. Standing waves are waves with the same amplitude and frequency travelling in the opposite direction. Longitudinal waves can also generate standing waves.
3. Do you find the velocity of sound in the air column or in the water column?
Answer: The sound velocity is determined in the air column, which is above the water column.
4. What are the possible errors in the result?
Answer: The following are two probable inaccuracies in the result:
Because the confined air in the air column is denser than the outside air, the air velocity may be reduced.
Humidity in the air above the confined water column may enhance sound velocity.
5. Will the result be affected if we take other liquids than water?
Answer: It will not be altered in any way.
FAQs on To Find the Speed of Sound in Air at Room Temperature Using a Resonance Tube By Two Resonance Positions
1. On what principle does the resonance tube work?
The idea of the resonance tube is based on the resonance of an air column with a tuning fork. Transverse stationary waves are formed in the air column. The wave's node is at the water's surface, while the wave's antinode is at the tube's open end.
2. Define the resonance of the air column?
The phenomenon of resonance is defined as the frequency of the air column is equal to the frequency of the tuning fork. A variable piston adjusts the length of a resonance air column, which is a glass tube. The two subsequent resonances seen at room temperature are at 20 cm and 85 cm in column length. Calculate the sound velocity in the air at room temperature if the length's frequency is 256 Hz.
3. During vibration, what are the types of waves being produced in the air column?
Longitudinal stationary waves are generated in the air column while measuring the speed of sound at room temperature.
4. What is end correction?
End correction is defined as the reflection of a sound wave from the end of the tube (slightly above it).
5. How do you find the velocity of sound in air?
It is found using the air column lying above the water surface.
6. What are some of the errors that can occur while calculating the result?
There are two majorly possible errors:
If the air enclosed inside is denser than the air outside, it can reduce the velocity of sound.
The velocity of sound can be increased if the air above the column has increased humidity.
Frequency of tuning fork v(Hz) | Resonance | No. of observations | Position of water level at resonance | Mean length (mean of three observations in column 4c) l (cm) | ||
Water level falling (cm) | Water level rising (cm) | Mean (cm) | ||||
512 | First | 1. 2. 3. | l₁’ = 16.1 | |||
Second | 1. 2. 3. | l₂’ = 50.3 | ||||
480 | First | 1. 2. 3. | l₁’’ = 17.3 | |||
Second | 1. 2. 3. | l₂’’ = 53.9 | ||||
( Note. The ideal observations are as samples.)
PhysicsOpenLab Modern DIY Physics Laboratory for Science Enthusiasts
Sound experiments.
May 13, 2019 English Posts 10,935 Views
The most obvious use for a sound card interfaced with a computer, along with a microphone and speakers, is to explore the physics of sound and the propagation of acoustic waves. The sound card and its use we have already described in the following post: Sound Card Applications . We now want to describe a series of simple experiences of sound waves physics that can be completed with a sound card, open software and a few other “low cost” components.
Measurement of Sound Speed in Air
With a sound card and two microphones it is relatively easy to measure the speed of sound. Recall that the speed of sound is the speed of a sound wave which propagates in an environment, called medium . The speed of sound varies depending on the medium (for example, the sound propagates faster in water than in air), and also varies with the properties of the medium, especially with its temperature.
This is a very important physical property, because it is also the speed of mechanical perturbations in a given substance.
In the air, the sound speed is 331 m/s at 0°C and 343.8 m/s at 20°C (and in linear approximation it varies according to the law a (T) = (331.45 + (0, 62 * T)) m/s with T the temperature measured in °C).
The measure consists in arranging the two microphones separated from each other by a known distance (which we will then vary) and in producing a sound of short duration (for example a snap) in a place in front of the microphones. The arrangement of the microphones is shown in the image below, the “lab jack” on the right is where the sound is produced by dropping a metal ball on the plate.
Obviously the acoustic waves will reach first the microphone 1 and then the microphone 2. Through the sound card and the two connected microphones (one on the left channel and the other on the right channel) and using the audacity software it is possible to acquire and display the two audio tracks, shown in the graphic below. We can see how the instant of arrival of the acoustic wave is temporally displaced for the two microphones. By measuring the time difference and knowing the distance between the two microphones it is possible to calculate the speed of the acoustic wave.
To better evaluate the time difference of arrival of the acoustic wave, samples can be exported and data can be acquired and displayed on Excel . Knowing the sampling frequency ( f = 44.1 KHz, T = 22.67 μs ) it is immediate to find the time difference.
By measuring for different distance values of the two microphones we can more accurately evaluate the speed of the acoustic wave by tracing the regression line, as shown in the graph below. We get the value of 347 m/s , very close to the real value of 344 m/s.
Stationary Waves and Resonance
The theory of sound tubes states that inside a tube of length L and diameter D , closed at one end, stationary resonance acoustic waves of frequency fn are formed and the frequency can be determined by the formula :
fn = (2n-1) * v/4L where n = 1,2,3,… v = sound speed
For a tube open at both ends, the formula for determining stationary frequencies is:
fn = n * v/2L where n = 1,2,3,… v = sound speed
To derive these formulas it is sufficient to consider the “boundary conditions” so that a stationary wave can be established inside the tube : for example at the point corresponding to the cap the variation of air displacement is set to zero, while at the point corresponding to the the tube open, the pressure variation is set to zero because the air is at atmospheric pressure. To obtain more precise results, however, it is necessary to take into account the “on-board effects” of the air near the pipe openings: in practice instead of length L the “effective length” must be used, which also takes into account the diameter D :
Lef = L + 0,8*D for an open tube
Lef = L + 0,4*D for a tube open on only one side
After this theoretical premise we briefly describe this simple experiment. A plastic tube about 1m long was used, at one end a microphone connected to the sound card was placed. The air in the tube was placed in “resonance” simply by blowing at the open end. Measurements were made both with the open tube and with the tube closed. The image below shows the experimental setup.
With audacity the audio track is recorded, image below as an example, and from this audio track the frequency spectrum of the sound emission is calculated.
The diagram below shows the aspect of the frequencies that are produced in the case of a tube open at both ends. In the following graph instead is shown the spectrum produced by a tube closed on one side. The peaks corresponding to the various harmonics that extend, with ever smaller amplitude, up to quite high frequencies, are very noticeable.
Doppler Effect
With our sound card and audacity software we can also easily make a qualitative demonstration of the doppler effect in acoustics. The Doppler effect is a physical phenomenon which consists in the apparent change, with respect to the original value, of the frequency or wavelength perceived by an observer reached by a wave emitted by a source that is in movement with respect to the observer himself . As we all know The Doppler effect can be seen by listening to the difference in the sound emitted by the siren of a rescue vehicle when it approaches and when it moves away, or that in the whistle of a train approaching before and then moving away.
For the theoretical explanation we refer to the numerous texts and websites that describe the phenomenon.
The experiment consists in using a simple buzzer with a battery attached to a rod and rotating this rod in front of the microphone connected to the sound card : in this way the buzzer will alternatively be approaching and moving away from the microphone.
For audio recording we use the audacity spectrogram function: this feature allows you to record and display the trend over time of the sound frequency spectrum, where the intensity is represented by the color. The image below shows the spectrogram of the sound emitted by the buzzer when it is stopped with respect to the microphone. The lines correspond to the various frequencies and we see how these are constant over time.
The following graphs show instead the spectrograms that are obtained when the buzzer is rotated. We see how the frequency of the harmonics, as they are recorded by the microphone, varies cyclically between a maximum and a minimum around the value that one has when stopped. This variation corresponds to the moments in which the buzzer approaches / moves away from the microphone.
The graph below shows the magnified spectrogram of a high frequency harmonic in which the frequency shift of the sound emission is more evident.
Sound Beats
Our sound card allows us to easily explore another interesting phenomenon: beats . In music theory, in physics and particularly in acoustics, beat is the frequency resulting from the superposition of periodic quantities, usually sinusoidal oscillations of different and near frequency. It is based on the properties of the superposition principle .
The phenomenon can easily be understood if we consider the mathematical sum of two sinusoidal functions (which represent two overlapping sounds):
The experiment is performed by placing two loudspeakers horizontally on supports, driven by an amplifier and function generator. The microphone connected to the sound card is placed in the intermediate space between the speakers. By varying the frequency of the sound emitted by the two speakers, the audio track is acquired, always with audacity software.
The graph below shows the beat produced by two sounds, in the left part the two sounds have very close frequencies, while in the right part of the graph the frequencies are more distanced and in fact the envelope function has a greater frequency.
If you liked this post you can share it on the “social” Facebook , Twitter or LinkedIn with the buttons below. This way you can help us! Thank you !
If you like this site and if you want to contribute to the development of the activities you can make a donation, thank you !
Tags Sound Card
Gamma Spectroscopy with KC761B
Abstract: in this article, we continue the presentation of the new KC761B device. In the previous post, we described the apparatus in general terms. Now we mainly focus on the gamma spectrometer functionality.
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.
| Medium | (m/s) |
|---|---|
| Air | 331 |
| Carbon dioxide | 259 |
| Oxygen | 316 |
| Helium | 965 |
| Hydrogen | 1290 |
| Ethanol | 1160 |
| Mercury | 1450 |
| Water, fresh | 1480 |
| Sea Water | 1540 |
| Human tissue | 1540 |
| Vulcanized rubber | 54 |
| Polyethylene | 920 |
| Marble | 3810 |
| Glass, Pyrex | 5640 |
| Lead | 1960 |
| Aluminum | 5120 |
| Steel | 5960 |
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.
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
- Authors: William Moebs, Samuel J. Ling, Jeff Sanny
- Publisher/website: OpenStax
- Book title: University Physics Volume 1
- Publication date: Sep 19, 2016
- Location: Houston, Texas
- Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
- Section URL: https://openstax.org/books/university-physics-volume-1/pages/17-2-speed-of-sound
© Jul 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.
Remember Me
Shop Experiment Speed of Sound Experiments
Speed of sound.
Experiment #28 from Physics Explorations and Projects
Introduction
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 may choose different methods, you will need to have a class discussion after the investigations to summarize the class’s findings.
- Design and perform an investigation.
- Draw a conclusion from evidence.
- Estimate the speed of sound.
- Experience measuring a quantity that does not fit into previous experimental models and requires a novel approach.
Sensors and Equipment
This experiment features the following sensors and equipment. Additional equipment may be required.
Ready to Experiment?
Ask an expert.
Get answers to your questions about how to teach this experiment with our support team.
- Call toll-free: 888-837-6437
- Chat with Us
- Email [email protected]
Purchase the Lab Book
This experiment is #28 of Physics Explorations and Projects . The experiment in the book includes student instructions as well as instructor information for set up, helpful hints, and sample graphs and data.
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.
Mach NumherThe 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 GasesThe 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:
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 EffectThe 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 FormulasThere 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
The Newton-Laplace formula works for both gases and liquids (fluids): v = (K s /ρ) 1/2
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
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 SoundThe 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 MarsThanks 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 ProblemsFind 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).
Related Posts Teacher Resource CenterPasco partnerships.  2024 Catalogs & BrochuresMeasuring the speed of sound with an echo. Students will first predict the speed of sound in the air of their classroom using a simple relationship accounting for temperature. Students will measure the time it takes a short pulse of sound to travel the length of a tube, reflect off the closed end, and return. Using this measurement, they will calculate the speed of sound and compare it to their prediction. Grade Level: High School Subject: Physics Student Files
Teacher Files Sign In to your PASCO account to access teacher files and sample data. Watch Video Measuring the Speed of Sound Using an EchoMeasure the time it takes a short pulse of sound to travel the length of a tube, reflect off the closed end, and return. Using this measurement, calculate the... Featured Equipment Resonance Air ColumnResonance tube with plunger, node markers and detachable stands for performing waves and sound experiments.  Wireless Sound SensorThe Wireless Sound Sensor measures sound wave forms and sound level in one compact and portable sensor.  Physics Starter Lab StationThis starter Lab Station includes the wireless motion, force, current and voltage sensors used to perform some of the key lab activities from the Physics Lab Station Investigations manual. Many lab activities can be conducted with our Wireless , PASPORT , or even ScienceWorkshop sensors and equipment. For assistance with substituting compatible instruments, contact PASCO Technical Support . We're here to help. Copyright © 2020 PASCO Source Collection: Lab #13 Physics Lab Station InvestigationsSource Collection: Lab #03 Physics Lab Station: Waves and SoundMore experiments.
High School
June 9, 2003 How were the speed of sound and the speed of light determined and measured?Chris Oates, a physicist in the Time and Frequency Division of the National Institute of Standards and Technology (NIST), explains. Despite the differences between light and sound, the same two basic methods have been used in most measurements of their respective speeds. The first method is based on simply measuring the time it takes a pulse of light or sound to traverse a known distance; dividing the distance by the transit time then gives the speed. The second method makes use of the wave nature common to these phenomena: by measuring both the frequency (f) and the wavelength () of the propagating wave, one can derive the speed of the wave from the simple wave relation, speed = f×. (The frequency of a wave is the number of crests that pass per second, whereas the wavelength is the distance between crests). Although the two phenomena share these measurement approaches, the fundamental differences between light and sound have led to very different experimental implementations, as well as different historical developments, in the determination of their speeds. In its simplest form, sound can be thought of as a longitudinal wave consisting of compressions and extensions of a medium along the direction of propagation. Because sound requires a medium through which to propagate, the speed of a sound wave is determined by the properties of the medium itself (such as density, stiffness, and temperature). These parameters thus need to be included in any reported measurements. In fact, one can turn such measurements around and actually use them to determine thermodynamic properties of the medium (the ratio of specific heats, for example). On supporting science journalismIf 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. The first known theoretical treatise on sound was provided by Sir Isaac Newton in his Principia, which predicted a value for the speed of sound in air that differs by about 16 percent from the currently accepted value. Early experimental values were based on measurements of the time it took the sound of cannon blasts to cover a given distance and were good to better than 1 percent of the currently accepted value of 331.5 m/s at 0 degrees Celsius. Daniel Colladon and Charles-Francois Sturm first performed similar measurements in water in Lake Geneva in 1826. They found a value only 0.2 percent below the currently accepted value of ~1,440 m/s at 8 degrees C. These measurements all suffered from variations in the media themselves over long distances, so most subsequent determinations have been performed in the laboratory, where environmental parameters could be better controlled, and a larger variety of gases and liquids could be investigated. These experiments often use tubes of gas or liquid (or bars of solid material) with precisely calibrated lengths. One can then derive the speed of sound from a measurement of the time that an impulse of sound takes to traverse the tube. Alternatively (and usually more accurately), one can excite resonant frequencies of the tube (much like those of a flute) by inducing a vibration at one end with a loudspeaker, tuning fork, or other type of transducer. Because the corresponding resonant wavelengths have a simple relationship to the tube length, one can then determine the speed of sound from the wave relation and make corrections for tube geometry for comparisons with speeds in free space. The wave nature of light is quite different from that of sound. In its simplest form, an electromagnetic wave (such as light, radio, or microwave) is transverse, consisting of oscillating electric and magnetic fields that are perpendicular to the direction of propagation. Moreover, although the medium through which light travels does affect its speed (reducing it by the index of refraction of the material), light can also travel through a vacuum, thus providing a unique context for defining its speed. In fact, the speed of light in a vacuum, c, is a fundamental building block of Einstein's theory of relativity, because it sets the upper limit for speeds in the universe. As a result, it appears in a wide range of physical formulae, perhaps the most famous of which is E=mc 2 . The speed of light can thus be measured in a variety of ways, but due to its extremely high value (~300,000 km/s or 186,000 mi/s), it was initially considerably harder to measure than the speed of sound. Early efforts such as Galileo's pair of observers sitting on opposing hills flashing lanterns back and forth lacked the technology needed to measure accurately the transit times of only a few microseconds. Remarkably, astronomical observations in the 18th century led to a determination of the speed of light with an uncertainty of only 1 percent. Better measurements, however, required a laboratory environment. Louis Fizeau and Leon Foucault were able to perform updated versions of Galileo¿s experiment through the use of ingenious combinations of rotating mirrors (along with improved measurement technology) and they made a series of beautiful measurements of the speed of light. With still further improvements, Albert A. Michelson performed measurements good to nearly one part in ten thousand. Metrology of the speed of light changed dramatically with a determination made here at NIST in 1972. This measurement was based on a helium-neon laser whose frequency was fixed by a feedback loop to match the frequency corresponding to the splitting between two quantized energy levels of the methane molecule. Both the frequency and wavelength of this highly stable laser were accurately measured, thereby leading to a 100-times reduction in the uncertainty for the value of the speed of light. This measurement and subsequent measurements based on other atomic/molecular standards were limited not by the measurement technique, but by uncertainties in the definition of the meter itself. Because it was clear that future measurements would be similarly limited, the 17th Conf¿rence G¿n¿rale des Poids et Mesures (General Conference on Weights and Measures) decided in 1983 to redefine the meter in terms of the speed of light. The speed of light thus became a constant (defined to be 299,792,458 m/s), never to be measured again. As a result, the definition of the meter is directly linked (via the relation c= f×) to that of frequency, which is by far the most accurately measured physical quantity (presently the best cesium atomic fountain clocks have a fractional frequency uncertainty of about 1x10 -15 ). |
IMAGES
VIDEO
COMMENTS
7. Calculate avg. 8. Calculate the speed of sound using avg for this tuning fork. 9. Repeat the above procedure for the other tuning fork. 10. Calculate an average value for the speed of sound. 11. Calculate a theoretical value for the speed of sound using: v = (331.50+0.61T)m/s (Eq. 7-3) where T is the temperature in degrees Celsius.
Measurement of the speed of sound propagation in air inside a {large} room is an approximation to this ideal situation. This experimental setup is shown in the pix below. The apparatus consists of using a narrow voltage pulse output from an Agilent 3320A Function Generator to excite a piezo-electric horn mounted at the LHS end of an optical ...
Past Papers. Edexcel. Religious Studies. Past Papers. OCR. Religious Studies. Past Papers. Revision notes on 4.9.10 Determining the Speed of Sound in Air in a Resonance Tube for the OCR A Level Physics syllabus, written by the Physics experts at Save My Exams.
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 ...
1. Measure the length of the resonance tube. Record the length on the datasheet. 2. With the speaker placed a few centimeters from one end of the tube, as shown in Fig. 1 Connect the speaker to the "Low Ω" outputs of the frequency generator, as shown in Fig. 2 and connect the "High Ω" outputs to "CH1" of the oscilloscope.
A variable piston adjusts the length of a resonance air column, which is a glass tube. The two subsequent resonances seen at room temperature are at 20 cm and 85 cm in column length. Calculate the sound velocity in the air at room temperature if the length's frequency is 256 Hz.
of the sound wave. In this experiment, you will be using different frequencies produced by a frequency generator interface to determine the velocity of sound in air. Since the frequencies used will be known, to calculate the velocity of sound you need to find the wavelength corresponding to that sound. By
EXPERIMENT 11 Velocity of Waves 2. Purpose To determine the speed of sound in air, and to find the relationship between the velocity of a wave in a string, the linear density, and the tension. You will do this by performing two different experiments: Part 1: Speed of Sound in Air IPart 2: Sonometer- Waves in a Stretched String
the speed of sound in air. Preliminaries. This experiment investigates the resonance conditions of a simple system consisting of a column of air closed at one end and driven at the other by an external speaker. Figure 1. Schematic for Standing Sound Waves Experiment . Any vibrating object that can compress and rarify a gas can produce traveling ...
temperature. The speed of sound is not a constant value! To calculate today's speed of sound, v,wewilldeter-mine the wavelength, (lambda), of the sound pro-duced by a tuning fork of known frequency, f: v = f (12.1) A vibrating tuning fork generates a sound wave that travels outward in all directions. When held above a sound tube, a portion of ...
Measurement of Sound Speed in Air. With a sound card and two microphones it is relatively easy to measure the speed of sound. Recall that the speed of sound is the speed of a sound wave which propagates in an environment, called medium. The speed of sound varies depending on the medium (for example, the sound propagates faster in water than in ...
Sound 8.1 Purpose In this experiment we will be using resonance points of a sound wave traveling through an open tube to measure the speed of sound in air. In order to understand how this can be done, we must discuss some properties of wave motion. 8.2 Introduction The type of waves that we will be concerned with in this experiment are what are ...
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.
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
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 ...
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.
Measure the speed of sound in air using a tube that is closed at one end. Use a Sound Sensor to record the initial pulse of sound and its echo. ... Calculate the speed of sound based on the overall distance traveled and the round-trip time. Providing educators worldwide with innovative solutions for teaching science. ... Toll Free: 1-800-772 ...
Speed of Sound in Physics. This entry was posted on June 17, 2023 by Anne Helmenstine (updated on June 22, 2023) The speed of sound in dry air at room temperature is 343 m/s or 1125 ft/s. In physics, the speed of sound is the distance traveled per unit of time by a sound wave through a medium. It is highest for stiff solids and lowest for gases.
Students will first predict the speed of sound in the air of their classroom using a simple relationship accounting for temperature. Students will measure the time it takes a short pulse of sound to travel the length of a tube, reflect off the closed end, and return. Using this measurement, they will calculate the speed of sound and compare it to their prediction.
In this experiment, we are going to use a tuning forkfor other experiments such as measuring the resistivity of a wire https://www.youtube.com/watch?v=sGhGR...
The first method is based on simply measuring the time it takes a pulse of light or sound to traverse a known distance; dividing the distance by the transit time then gives the speed. The second ...
Learn how to use a starting pistol, a stopwatch and a trundle wheel to estimate the speed of sound in air. The web page explains the method, the assumptions and the formula involved in this simple experiment.