Sound: production, transmission, speed and echoes: WASSCE Physics

Thunder rumbles seconds after the lightning. A drum's skin shakes as it sounds. You cannot hear across the vacuum of space. Sound is a mechanical wave, and its behaviour follows directly from that one fact.

Learning objectives

By the end of this lesson you should be able to:

explain how sound is produced and transmitted
show that sound needs a material medium (bell-jar experiment)
compare the speed of sound in solids, liquids and gases, and state the factors affecting it in air
solve echo problems and describe a method of measuring the speed of sound

Production of sound

Definition

Sound is a form of energy produced by vibrating bodies and transmitted as a longitudinal wave through a material medium.

Every sound source vibrates: a guitar string, the skin of a drum, a loudspeaker cone, the prongs of a tuning fork, the vocal cords in your throat. Touch a vibrating tuning fork to water and it splashes; place your fingers on your throat as you hum and you feel the vibration.

How sound travels

The vibrating source pushes on the neighbouring air molecules, squeezing them together (a compression) and then pulling back, leaving a region of low pressure (a rarefaction). These compressions and rarefactions pass from molecule to molecule. Each molecule only vibrates to and fro about its position, parallel to the direction of travel: sound is a longitudinal wave.

Sound needs a medium

The bell-jar experiment:

An electric bell is hung inside a glass bell jar connected to a vacuum pump, and switched on. It is heard clearly.
As air is pumped out, the sound grows fainter, although the hammer can still be seen striking the gong.
When most of the air has been removed, almost nothing is heard.
Letting air back in makes the sound return.

Conclusion: sound needs a material medium; it cannot travel through a vacuum. (Light can, which is why the bell is still seen.)

Speed of sound

Medium	Approximate speed / m s⁻¹
Air (0 °C)	330
Air (20 °C)	343
Water	1500
Steel	5000

Sound travels fastest in solids, slower in liquids and slowest in gases, because the particles are closer together and more strongly bound in solids.

Factors affecting the speed of sound in air

Temperature: speed increases with temperature (about 0.6 m s⁻¹ per °C).
Humidity: speed increases slightly in humid air.
Wind: sound travelling with the wind arrives sooner.
Pressure has no effect (at constant temperature).

In Sierra Leone

During a thunderstorm in the rainy season, count the seconds between the flash and the thunder and divide by 3 to estimate the distance in kilometres. Light arrives almost instantly; sound covers about 1 km every 3 seconds.

Echoes

Definition

An echo is a reflected sound heard after the original sound.

For the echo to be heard separately, it must arrive at least about 0.1 s after the original sound. In air at 340 m s⁻¹, this means the reflecting surface must be at least about 17 m away (the sound travels 34 m there and back).

Echo equation: the sound travels to the reflector and back, so

v = \dfrac{2d}{t} \qquad d = \dfrac{vt}{2}

Worked example

A girl claps her hands 85 m from a cliff and hears the echo 0.5 s later. Find the speed of sound.

v = \dfrac{2d}{t} = \dfrac{2 \times 85}{0.5} = 340\ \text{m s}^{-1}

\begin{aligned}v &= \dfrac{2d}{t} \\ &= \dfrac{2 \times 85}{0.5} \\ &= 340\ \text{m s}^{-1}\end{aligned}

Common mistake

Do not forget the factor of 2: an echo travels the distance twice (there and back). Using $v = d/t$ gives half the true speed.

Worked example

A man stands between two cliffs. He hears the first echo after 1.5 s and the second after 2.5 s. If sound travels at 340 m s⁻¹, how far apart are the cliffs?

Distance to the nearer cliff $= \dfrac{340 \times 1.5}{2} = 255$ m. To the farther cliff $= \dfrac{340 \times 2.5}{2} = 425$ m.

Separation $= 255 + 425 = 680$ m.

Measuring the speed of sound by echoes

Stand at least 50 m from a large wall, measuring the distance $d$ with a tape.
Clap and adjust the clapping rate until each clap coincides with the echo of the previous one.
A second person times 20 or more claps. The time between claps $t$ is the time for sound to travel $2d$ .
$v = \dfrac{2d}{t}$ .

Key points

Sound is produced by vibrating bodies and travels as a longitudinal wave.
Sound needs a material medium; it cannot cross a vacuum (bell-jar experiment).
Speed: solids > liquids > gases; in air about 330–340 m s⁻¹, increasing with temperature.
Echo: $v = \dfrac{2d}{t}$ ; a separate echo needs a reflector at least about 17 m away.

WASSCE examination focus

WAEC tests this

Describe the bell-jar experiment and state its conclusion, explain why sound travels faster in solids, give the factors affecting the speed of sound in air, and solve echo problems (often a man between two cliffs or a gun fired near a wall). Show the factor of 2 clearly.

Quick check

Why can astronauts on the Moon not talk to each other directly?
An echo from a cliff returns after 2 s. If sound travels at 330 m s⁻¹, how far away is the cliff?
Does the speed of sound in air increase or decrease with temperature?

Answers: 1. There is no air (a vacuum), and sound needs a material medium. 2. $d = \dfrac{330 \times 2}{2} = 330$ m. 3. It increases.

Sound: production, transmission, speed and echoes