# Activity: Sound waves

#### Aims

• Introduce sound as a longitudinal wave.
• Investigate the wave nature of sound.
• Derive the equations for the harmonic frequencies of standing waves in pipes.
• Measure the speed of sound.

#### Doing this at home

The required experiment Speed of sound (drinking straw) uses just a drinking straw and the program Audacity so can easily be done at home. The extension work is simulation based.

#### Pressure waves

When air is disturbed it causes a change in pressure which in turn disturbs the surrounding air resulting in propagation of changing pressure throughout the medium. This can be simulated using Algodoo.

In the simulation you can see the disturbance spreading down the tube.

• How would you describe the motion of the gas molecules?
• How can you tell that energy is transferred?
• Does the pulse reflect off the left end?
• Explain why the speed of sound is dependent on the temperature.

If the end is made to move with SHM then a continuous wave will be sent along the tube, the individual molecules wouldn't oscillate but layers of molecules would. This can be demonstrating by observing a candle flame licker when placed next to a loud speaker, here the flicker is shown in slow motion.

https://youtu.be/TuOpSD-cXMc

Notice how the flames move in the same direction as the wave, this means sound is a longitudinal wave.

It is often more convenient to represent the displacement of the layers of gas rather than the changing pressure. Use the simulation below to investigate the relationship between the wave and the displacement position graph.

Notice how there is a zero displacement at the centre of a compression and rarefaction.

• Where is the maximum pressure?

Sound is not just something to be measured it can also be experienced with our senses, the loudness and pitch of a sound are related to the physical quantities of amplitude and frequency

High pitch > High frequency
Loud > Large amplitude
Speed = 340 ms-1

Use the simulation below to investigate frequency and amplitude. The graphs are displacement time graphs.

• Calculate the wavelength of a 600 Hz sound.

Reflection

Reflection of sound is called an echo, a room with no reflection is called an anechoic chamber.

Some interesting TOK aspects in that video, how our physical environment affects the way we think (or not).

Refraction

Refraction of sound isn't an everyday experience but if you are ever sitting in a boat on a still evening you might notice that sounds seem amplified and this is due to refraction. On a still evening the cold air settles near the water with the warmer air on top. Sound waves travelling up through the air are refracted so much by the different layers that they are directed back down again. What you hear is the sound directly from the source plus the sound refracted down.

This can be demonstrated in the ripple tank simulation.

Here you can see the different layers. The wave speed increases with increasing height.

#### Diffraction

We have seen (or maybe heard) that sound reflects and refracts, this often hides other effects such as diffraction. Imagine your teacher is talking in the classroom with the door open. If you go down the corridor you will still hear your teacher but it will be because of reflection off the walls not diffraction through the door. In an open space you may notice how sound diffracts around objects, this is something that animators have to be aware of when adding sound to computer games.

The diffraction of waves around an object can also be simulated with the ripple tank.

Interference

Another rarely experienced phenomena so today is your lucky day. If you have stereo speakers set them up about 1 m apart (if not you will have to make do with the speakers in your laptop. Using the simulation above (making waves) play a note through the speakers. Place a finger in one ear and move around the room. You should be able to hear quiet and loud areas. This is due to interference.

You can also simulate this here PhET sound

#### Standing waves in closed pipes

You have seen that a sound wave reflects off the end of a pipe, when  a reflected wave adds with the incident wave a standing wave can be formed.

• A node is a position of zero displacement. Why is a node formed at the closed end?

The simulation below shows the possible waves (harmonics) in a closed pipe, use the slider to change between harmonics. Note the position of the nodes.

1st Harmonic

• Given that the pipe length is L what is the wavelength of the first harmonic?
• If the velocity of sound is v what is the frequency of the first harmonic?

3rd Harmonic

• What is the wavelength of the 3rd harmonic?
• Show that the frequency of the 3rd harmonic is 3 x the frequency of the 1st.
• Why are only odd harmonics possible?

#### Standing waves in open pipes

An open pipe has antinodes at each end.

1st Harmonic

• Given that the pipe length is L what is the wavelength of the first harmonic?
• If the velocity of sound is v what is the frequency of the first harmonic?

2nd Harmonic

• What is the wavelength of the 2nd harmonic?
• Show that the frequency of the 2nd harmonic is 2 x the frequency of the 1st.
• Why are all the harmonics possible but only odd ones were possible in the closed pipe?

Here is a not a physics teacher demonstrating on a trumpet.

#### Measuring the speed of sound

Speed of sound (drinking straw)

Post a screenshot of your graph of wavelength vs 1/frequency including error bars and best fit lines.

Give the value for the speed of sound including uncertainties.

Words: 1-159

And some extension work if you feel inclined

Waves in pipes simulation

Standing waves simulation (GeoGebra)

There are also some exercises on page 181

Now know