experiments to measure the speed of sound in air

• 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!

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How to Measure Sound Travel in the Air

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Key Takeaways

• Sound can travel through air, water and solids but not through a vacuum, as it requires a medium to propagate.
• The speed of sound in air is approximately 1,130 feet (344 meters) per second at room temperature, though this speed can vary with changes in temperature and humidity.
• You can perform a simple experiment involving two blocks of wood, a stopwatch and a tape measure to measure the speed of sound in air by calculating the time it takes for the sound to travel a known distance.

Sound can travel through most materials -- the most commonly known being air (gas), water (liquid) and steel (solid). However, it does not travel at all in a vacuum, because the sound waves need some kind of medium in which to travel. In addition, some materials absorb, rather than reflect or pass, sound waves. This is the basis of soundproofing [source: Kurtus ].

The average speed of sound through air is about 1130 feet per second (344 meters per second) at room temperature. However, changes in temperature and humidity will affect this speed [source: Kurtus ].

Here is a simple way to measure the speed at which sound travels through air. You'll need the following items:

• Two blocks of wood, or other items that make a loud, sharp sound when struck together
• A stopwatch
• A friend to help with the experiment
• A tape measure

Instructions:

• Find a large empty area, such as a field or large court.
• Choose two spots on opposite ends of the area where each person will stand.
• Measure the distance between the two spots using a tape measure. Alternatively, you can count off measured steps between the two spots.
• Have your friend take the blocks and stand at one spot, holding them up high.
• Take the stopwatch and stand at the other spot. Make sure you have a clear view of the blocks.
• Signal your friend to bang the two blocks together hard.
• Start the stopwatch as soon as you see the blocks hit each other.
• Press stop as soon as you hear the sound from the blocks.
• Calculate the speed of the sound by dividing the distance between you and your friend by the elapsed time. To get a more accurate measurement, repeat the above steps a few times and then take an average of the results [source: Green Planet Solar Energy ]. //]]]]> ]]>

Frequently Asked Questions

How does the humidity level affect the speed of sound in air, can the speed of sound vary at different altitudes.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

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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• 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. 

( Note. The ideal observations are as samples.)

Measuring the speed of sound in air using a smartphone and a cardboard tube

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Speed of sound in air.

The purpose of this activity is to 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.

Grade Level: College • High School

Subject: Physics

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Measurement of the speed of sound in air

A column of air in a tube, closed at one end, has a natural frequency of vibration at a particular length. If a vibrating tuning fork is placed over the tube and the length of the column of air is altered, it is possible to find the length that resonates with the tuning fork. At this point a loud sound is heard. In it's fundamental mode of vibration the length of the air column is approximately equal to one quarter of a wavelength. By measuring the length of the air column (l) and the diameter of the tube (d) it is possible to calculate the speed of sound in air (c) using the formula: c = 4f ( l + 0.3d), where f is the frequency of the tuning fork. Note: In this simulation I have not included sound, so the position of resonance is found from the shape of the wave (1/4 wave).

• Press the "Strike Fork" button.
• Adjust the height of the inner tube, using the slider, until resonance occurs. You will recognise resonance (at 1/4 wavelength) when the wave pattern produces a curved V shape.
• At resonance, press the "Get Ruler" button. Record the length (l) from the top of the water to the top of the tube and the frequency of the tuning fork.
• Press "New Fork". Record the frequency f.
• Repeat steps 1 to 3 until you have got a resonant length for each tuning fork.
• Ensure that your eye is level with the top of the tube when measuring the length to avoid parallax error.
• In the lab repeat your efforts to find the loudest resonance position for each tuning fork.