Speed of Sound
Introduction

In old westerns, cowboys often put their ear to a railway track to hear if a train is coming. This is because the speed of sound waves depends upon the material through which they are travelling. Sound travels 15 times faster through the metal railway tracks than through air, giving the cowboy an early warning of the train's arrival.
How fast is sound?
Have you ever been swimming in the sea when a boat goes past a long way off? You can hear the motor sooner and much more clearly underwater than above the water. Look at the table in Fig.1 to work out why.


Material Speed of sound (m/s)
Vacuum Does not travel
Air 330
Water 1500
Metal 5000

Figure 1.  The speed of sound in different materials.

Which of these materials does sound travel fastest in?
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Sound travels fastest in solids. This is because the molecules in solids are close together, which makes it easier for the vibrations to pass from one
molecule
A molecule is a group of atoms bonded together.
molecule
to the next.

The relationship between the
speed
Speed is a measure of how fast something is moving. It is calculated by dividing the distance travelled by the time taken.
speed
,
frequency
In general, the frequency of an event describes how often it occurs. When talking about waves, the frequency is a measure of how many waves go past a fixed point in a given time.
frequency
, and
wavelength
The wavelength of a wave is the distance from one peak to the next, or from one trough to the next.
wavelength
of sound is the same as for other waves:


We can use this equation to work out the wavelength of a particular sound wave, or a certain note.

The frequency of the musical note middle C is 261 Hz.

What is the speed of sound in air? (Look at the table above.)
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The wavelength is found by dividing the speed by the frequency:



The frequency of the musical note A is about 440 Hz. It has a higher pitch and a higher frequency than middle C.

What is the wavelength of the musical note A?
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Is this longer or shorter than the wavelength of middle C?
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Measuring the speed of sound
A common way to measure the speed of sound is to set up two microphones that are both attached to an electronic timer. A loud noise is made near the first microphone and the timer starts. The sound wave then travels towards the second microphone. When the wave reaches the second microphone, the timer stops. If you know the distance between the two microphones you can work out the speed of sound.


The distance between the two microphones is 20 m. Sound travels at 330 m/s in air. Click on the t in the equation above to rearrange it. Then use the equation to work out how long the sound takes to travel between the two microphones.

How long does it take the sound to get from one microphone to the other?
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Which of these methods would not give a more accurate measurement of the speed of sound?
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Sonic booms
Nothing can travel faster than light. However, some aeroplanes can fly faster than sound. We say that they can pass through the sound barrier. When planes fly this fast, they create a sonic boom. This is a very loud booming sound wave that can be heard for miles. It is very similar to the wake made behind a fast-moving boat.

Figure 2.   Sound waves being emitted from a slow-moving plane
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Figure 3.   Sound waves being emitted from a fast-moving plane
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Figure 4.   A photograph of the sound waves coming from a plane travelling faster than the speed of sound.
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The animation in Fig.2 shows a plane flying slower than the speed of sound. You can see that all the circles (wavefronts) remain inside each other. The plane in Fig.3 is moving faster than the speed of sound. The wavefronts generated by this plane overlap and form a cone in which the waves pile on top of each other (interfere constructively). This leads to the high intensity sound of a
sonic boom
A sonic boom is the loud booming noise created when a moving object travels faster than the speed of sound. It is caused by constructive interference of overlapping sound waves.
sonic boom
.

Summary


Sound waves travel fastest in solids and slowest in gases.

The speed of sound can be measured in a laboratory using microphones and an electronic timer.

A sonic boom is created when a moving object travels faster than the speed of sound.

Exercises
1. During a thunderstorm, you see a flash of lightning. Several seconds later, you hear the associated thunder. Why is this?
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2. Select the correct material to complete the paragraph below.

  • Sound waves travel slowest through a and fastest through a . Sound waves travel at an intermediate speed through a . Sound does not pass through a at all.
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3. A sound wave has a frequency of 500 Hz. In air, the speed of this wave is 330 m/s. What is the wavelength of this sound wave?
  • cm
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4. The same sound wave travels through a solid at a speed of 4000 m/s. What is the wavelength of the wave now?
  • m
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5. A sound wave traveling in water has a speed of 1500 m/s and a wavelength of 6 cm. What is the frequency of this sound wave?
  • Hz
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6. This sound wave passes into air. Its frequency does not change, but its speed changes to 330 m/s. What is the wavelength of the wave in air?
  • cm
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A method of measuring the speed of sound in air involves using two microphones both connected to an electronic timer. The timer measures how long the sound takes to travel between the two microphones. The experiment is repeated 10 times and the results are shown in the table below.


Experiment number 1 2 3 4 5 6 7 8 9 10
Time for the sound to travel (ms) 4.6 4.5 4.4 4.6 4.3 4.5 4.4 4.8 4.5 4.4

7. What units of time are used in the table above?
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8. What is the average time taken for the sound to travel between the two microphones? Express your answer in ms and s.
  • ms    s
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9. The distance between the two microphones is measured as 1.5 m. What is the
average speed
The average speed of an object is the distance travelled in a relatively long time interval divided by that time.
average speed
of sound for this experiment?
  • m/s (to the nearest whole number).
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10. What would you expect to happen if the two microphones were kept the same distance apart and placed into a large tank filled with water?

  • The measured time would .

    The calculated speed of the sound would .
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Figure 5.  
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11. Fig.5 above shows how
sound waves
Sound is carried by a wave and needs a material to travel through. Sound waves are longitudinal and are produced by vibrating sources such as musical instruments.
sound waves
can be used to measure how deep the water beneath the boat is. The boat makes a sound and then detects the echo 2 seconds later. The waves travel at 1500 m/s. How far have the waves travelled in this time?
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12. How deep is the water in Fig.5?
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13. What must be the speed of a plane for it to create a sonic boom?
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14. Which wave effect below leads to the high intensity of a sonic boom?
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