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# Success in Maths and Science unlocks opportunities

## 10.2 Speed of sound (ESACZ)

The speed of sound depends on the medium the sound is travelling in. Sound travels faster in solids than in liquids, and faster in liquids than in gases. This is because the density of solids is higher than that of liquids which means that the particles are closer together. Sound can be transmitted more easily.

The speed of sound also depends on the temperature of the medium. The hotter the medium is, the faster its particles move and therefore the quicker the sound will travel through the medium. When we heat a substance, the particles in that substance have more kinetic energy and vibrate or move faster. Sound can therefore be transmitted more easily and quickly in hotter substances.

Sound waves are pressure waves. The speed of sound will therefore be influenced by the pressure of the medium through which it is travelling. At sea level the air pressure is higher than high up on a mountain. Sound will travel faster at sea level where the air pressure is higher than it would at places high above sea level.

 Substance v ($$\text{m·s^{-1}}$$) aluminium $$\text{6 420}$$ brick $$\text{3 650}$$ copper $$\text{4 760}$$ glass $$\text{5 100}$$ gold $$\text{3 240}$$ lead $$\text{2 160}$$ water, sea $$\text{1 531}$$ air, 0℃ $$\text{331}$$ air, 20℃ $$\text{343}$$

Table 10.1: The speed of sound in different materials.

The speed of sound in air, at sea level, at a temperature of 21℃ and under normal atmospheric conditions, is $$\text{341}$$ $$\text{m·s^{-1}}$$.

## Measuring the speed of sound in air

### Aim

To measure the speed of sound.

### Apparatus

• Starter's gun or anything that can produce a loud sound in response to visible action

• Stopwatch

### Method

The speed of sound can be measured because light travels much faster than sound. Light travels at about $$\text{300 000}$$ $$\text{m·s^{-1}}$$ (you will learn more about the speed of light in the next chapter) while sound only travels at about $$\text{300}$$ $$\text{m·s^{-1}}$$. This difference means that over a distance of 300 m, the light from an event will reach your eyes almost instantly but there will be an approximate half a second lag before you hear the sound produced. Thus if a starter's pistol is fired from a great distance, you will see the smoke immediately but there will be a lag before you hear the sound. If you know the distance and the time then you can calculate the speed (distance divided by time). You don't need a gun but anything that you can see producing a loud sound.

Try this:

1. Find a place where you know the precise, straight-line distance between two points (maybe an athletics track)

2. Someone needs to stand at the one point to produce the sound

3. Another person needs to stand at the other point with the stop watches

4. The person with the stopwatch should start the stopwatch when they see the other person make the sound and stop the stopwatch when they hear the sound (do this a few times and write the times down)

### Results

You can now calculate the speed to sound by dividing the distance by the time. Remember to work in S.I. units (metres and seconds). If you took multiple readings then you can sum them and divide by the number of readings to get an average time reading. Use the average time to calculate the speed:

$v = \frac{D}{t}$
 Time (s) Distance (m) $$\text{m·s^{-1}}$$ Averages

### Conclusions

• What is your reaction time on the stopwatch? You can test this by starting it and then trying to stop it immediately.

• What was the forecast temperature on the day of the measurement?

• Was it humid or very dry?

Discuss what might change the speed of sound that you measured.

You can vary this experiment by trying it on days when the weather is different as this can change air pressure and temperature.

When the sound waves collide with an object they are reflected. You can think of the individual particles that are oscillating about their equilibrium position colliding into the object when the wave passes. They bounce off the object causing the wave to be reflected.

In a space with many small objects there are reflections at every surface but they are too small and too mixed up to have an outcome that a human can hear. However, when there is an open space that has only large surfaces, for example a school hall that is empty, then the reflected sound can actually be heard. The sound wave is reflected in such a wave that the wave looks the same but is moving in the opposite direction.

This means that if you stand in a hall and loudly say “hello” you will hear yourself say “hello” a split second later. This is an echo. This can also happen outdoors in a wide open space with a large reflecting surface nearby, like standing near a mountain cliff in an area with no trees or bushes.

This is a very useful property of waves.

Ships on the ocean make use of the reflecting properties of sound waves to determine the depth of the ocean. A sound wave is transmitted and bounces off the seabed. Because the speed of sound is known and the time lapse between sending and receiving the sound can be measured, the distance from the ship to the bottom of the ocean can be determined, This is called sonar, which is an acronym for Sound Navigation And Ranging.

## Worked example 1: SONAR

A ship sends a signal to the bottom of the ocean to determine the depth of the ocean. The speed of sound in sea water is $$\text{1 450}$$ $$\text{m·s^{-1}}$$. If the signal is received $$\text{1,5}$$ $$\text{seconds}$$ later, how deep is the ocean at that point?

### Identify what is given and what is being asked

\begin{align*} s & = \text{1 450}\text{ m·s$^{-1}$} \\ t & = \text{1,5}\text{ seconds} \text{ there and back} \\ \therefore t & = \text{0,75}\text{ seconds} \text{ one way} \\ D & = ? \end{align*}

### Calculate the distance

\begin{align*} \text{Distance } & = \text{ speed } \times \text{ time } \\ D & = s \times t \\ & = (\text{1 450}\text{ m·s$^{-1}$})(\text{0,75}\text{ s}) \\ & = \text{1 087,5}\text{ m} \end{align*}