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School-college Physics Notes: SOUND 6. Measuring the speed of sound

SOUND  6. Experiments to measure the speed of sound in air and a solid - synchronised microphones, echo times, tensioned wire-standing wave methods

Doc Brown's Physics exam study revision notes

6. Experiments to measure the speed of sound in air and a solid

(a) Using synchronised microphones to measure the speed of sound in air The experiment is performed by connecting a loud speaker to a signal generator to generate the sound to be picked up by the microphones.

You select a particular known specific frequency e.g. 250 Hz (f in Hz).

Two microphones are connected to an oscilloscope which pick up the sound from the speaker and which is converted to an electrical signal by the microphone and displayed as a trace on the cathode ray oscilloscope screen.

You can secure the speaker and two microphones with stands and clamps making sure they are aligned at the same height.

You set up the oscilloscope to detect the sound wave signals from both microphones - to give you two traces on the screen.

You start with the two microphones next to each other near the speaker.

You then slowly move one microphone away from the other.

When the two microphones are first exactly one wavelength apart, the two signal traces on the oscilloscope are exactly aligned - synchronised, as in the diagram above.

The trace from the microphone 2, furthest away from the speaker, will show a smaller amplitude - the diagram does not take this into account!

You then measure the distance between the microphones and this gives you the wavelength of the sound.

This is because the sound waves are aligned in phase and just one wavelength apart.

speed of sound wave (m/s) = frequency of sound (Hz) x wavelength of sound wave (m)

in 'shorthand'    v = f x λ

you know the frequency in Hz from the signal generator setting

and the wavelength is the distance between the microphones in cm ==> m

You repeat the experiment to calculate the average wavelength to give statistically the best result.

You can then repeat the experiments with other frequencies from the signal generator and you should find the speed stays the same, but, as the frequency is increased the wavelength of the sound wave should get shorter.

(b) Echo method to measure the speed of sound in air

You need two people to do the experiment.

Measure a distance d, e.g. 50 m from a tall wall or a building with a broad flat wall that will act as a sound wave reflector.

You then clap two pieces of flat wood together and adjust the rate of clapping until the sound of the claps are synchronised with the return of the echo.

Use a stopwatch to find the time interval between the claps e.g. measure the time of 10 claps and compute average.

Calculation of speed of sound in air.

If d = distance to wall (m), if t = average time interval between claps (s)

v = 2d/t (m/s)

Note that the distance is doubled because the sound is 'going there and back' in the time interval t.

This is not an accurate method, the clapping can't be done in perfect harmony, but its a bit of fun doing it.

Example of speed of sound calculation based on an echo

Suppose two students measured the following data.

The side of the school sports hall was 80 m away from the clapper.

50 claps took a total time of 24.2 s

v = 2d/t (m/s), d = 2 x 80 = 160 m, average clap time = 24.2 / 50 = 0.485 s

speed of sound v = 160 / 0.485 = 330 m/s (3 sf)

(c) An experiment to measure the speed of sound in air using a stretched string or wire.

In this method you use a mechanical vibrator (vibration transducer) to vibrates a tensioned (stretched) steel wire or elastic cord.

The vibrator, whose frequency is controlled by the signal generator, continuously transfers energy to the wire/cord making it vibrate.

This sends transverse waves down the wire/cord and produces a particular note when the wire/cord vibrates with specific number of wavelengths along the length of the wire.

The experimental set-up is shown below. The wire/cord is fixed to the vibration transducer and stretched horizontally over a pulley and tensioned with weights on the end.

You switch on the signal generator and observe the vibrations in terms of numbers of wavelength as you slowly increase the frequency.

You note the frequency when the vibrations seem 'stable' and a number of wavelengths can be clearly observed from the stable wave 'pattern'.

You count the number of waves along the wire/cord and the frequency displayed on the signal generator.

Things are a bit blurred so you need to take care in your observations and note that when stable, the wire seems to vibrate up and down and there seems to be points on the wire which don't seem to move up and down (these points are called nodes where the amplitude is at a minimum amplitude).

e.g. from the diagram 3 wavelengths = 60 cm, one wavelength = 20 cm or 0.20 m at a frequency of 1650 Hz.

speed = wavelength x frequency

speed of sound in air = 0.20 x 1650 = 330 m/s

You can repeat the experiments with different frequencies to produce ½, 1, 1½, 2, 2½, 3, 3½, 4 etc. wavelengths as you increase the frequency from the signal generator.

You can measure the number of wavelengths for each frequency, and you should get the same speed of sound in air, even though the note you hear changes.

You can experiment with different 'string' materials and different tension weights on the end of the wire.

You can also employ a bridge ↑ over which the wire is stretched, so you can vary the length of the vibrating wire.

A simple home experiment to show a standing wave in an elastic cord    I stretch a 30 cm (0.30 m) thick rubber band above a wooden base and clamped it in position on wooden blocks (upper photographs) and illuminated with a couple of suspended LED torches.

You can see, in the lower photographs, the two extremes (maximum amplitude) the rubber band reaches when tugged back and released to vibrate at its fundamental frequency.

The sound produced was rather 'dull', but using the speed of sound (v) as 330 m/s, you can calculate the frequency of oscillation of the rubber band.

The wavelength (λ) = 2 x 0.30 = 0.60 m

This is elastic cord length is doubled because the half-wave doubles back on itself to give a complete wavelength of the standing wave - the natural wavelength and frequency resulting from the particular mass, length and tension of the elastic cord (see animation below).

v = f x λ,  f = v / λ = 330 / 0.60 = 550 Hz  (hence the blurred photograph). This calculation oversimplifies the situation, but it is correct in principle!  The note was not clearly heard, but on stretching the same elastic band over an empty circular tin can of ~30 cm diameter, with a similar tension, a note could be clearly heard!

The note was theoretically between C5 and D5 on the musical frequency scale.

Standing waves are illustrated by the wave 'pictures on the left'.

They correspond in length to ½, 1, 1½, 2, 2½ and 3 wavelengths.

The animation is from https://en.wikipedia.org/wiki/String_vibration

(d) A simple experiment to measure the speed of sound in a solid

Introduction to the experiment

You can measure the speed of sound waves in a solid by measuring the frequency of sound waves produced when you hit a solid.

The method works best by hitting metal rods that will resonate strongly, mainly with one particular 'note' called the fundamental natural frequency - think of a tuning fork or musical triangle in music.

When you hit the rod, longitudinal sound waves are induced in the metal and they will also vibrate the surrounding air.

These sound wave frequencies can be picked up by a microphone and displayed on the screen of an oscilloscope.

You can pick out this fundamental natural frequency from other frequencies because it should give the highest amplitude signal. The experimental set-up

A uniform rod of metal of known length is suspended from its mid-point in a horizontal position.

The rod (length L) needs to at least 50 cm long and a few cm in diameter made of e.g. aluminium, brass or iron.

Near one end of the rod is placed a microphone connected to an oscilloscope and a hammer at the ready!

The oscilloscope is used to monitor both the amplitude and frequency of the sound waves produced when the rod is hit with the hammer.

Experimental procedure

This is a very technical experiment to do!

The rod is hit at one end with the hammer so it vibrates continuously making sound.

Tune in the oscilloscope to the frequency range of greatest amplitudes.

Record the frequency as best you can that corresponds to the highest amplitude on the screen.

Repeat several times to get the average frequency - the best value you can obtain.

A bit of theory before the speed calculation

When the rod is hit, its vibrations produce lots of difference frequencies.

However, all objects have a natural vibrational frequency that sets up a longitudinal standing wave that should give the maximum amplitude of sound.

This particular frequency is called the fundamental mode of vibration.

A standing wave does not vary its amplitude profile i.e. it doesn't appear to move - stationary.

What you see is one wave occupying twice the length of the rod.

I've shown this on the diagram in the cyan inset box below the rod.

The wavelength of this fundamental standing wave is equal to double the length of the rod.

(A point where the amplitude is zero is called a node - don't need to know this point for GCSE physics.)

An example of calculating the speed of sound in the rod

Suppose the rod is made of aluminium, diameter 2 cm and length 65 cm.

If the maximum amplitude was found to be at ~4.0 kHz, calculate the speed of sound in aluminium.

wavelength = 2 x L = 65 x 2 = 130 cm = 1.3 m

frequency = 4.0 kHz = 4000 Hz.

speed = frequency x wavelength = 4000 x 1.3 = ~5200 m/s

Note that the speed of sound in solids is much greater than in gases like air (~340 m/s).

Keywords, phrases and learning objectives for sound waves

Be able to interpret, describe or explain experiments to measure the speed of sound in air or solid.

Know the use of synchronised microphones, echo timing, tensioned wire-standing wave methods to measure the speed of sound in the school laboratory - the apparatus and lab procedure and any calculations based on observations-data.

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