Reflection of sound and echoes

Your voice comes back

Shout in front of a cliff or a big building, and a moment later you hear your own voice. Sound is reflected by hard surfaces, the way a ball bounces off a wall. The reflected sound we hear is an echo.

The laws of reflection

Sound obeys the same rules as light: the angle at which it hits a surface equals the angle at which it leaves, and both rays and the normal lie in one plane.

When can we hear an echo?

Our brain keeps a sound for about $0.1\ \text{s}$. An echo that returns sooner mixes with the original. In $0.1\ \text{s}$, sound in air travels $34\ \text{m}$, there and back, so the wall must be at least

away. The time for an echo from a wall at distance $d$ is

You should find that the echo time grows in step with the distance. Below about $17\ \text{m}$ the time is under $0.1\ \text{s}$, and the "time beyond $0.1\ \text{s}$" turns negative: no separate echo.

Reverberation

In a big hall with hard walls, sound is reflected again and again, and each word lingers: reverberation. Too much blurs speech, so halls use curtains, carpets and soft panels that absorb sound.

Uses of reflected sound

• A megaphone and a horn send the sound forward by reflecting it from their sides.
• A stethoscope carries the sound of the heart along its tube by many reflections.
• Curved ceilings and a board behind a stage reflect sound towards the audience.

Watch out. For an echo, always halve: the time is for the trip there and back.

A worked example

A boy claps $85\ \text{m}$ from a tall building. After how long does he hear the echo? Is it separate?

1. The path. There and back: $2 \times 85\ \text{m} = 170\ \text{m}$.
2. The time. $t = \dfrac{170\ \text{m}}{340\ \text{m/s}} = 0.5\ \text{s}$.
3. Separate? Yes: $0.5\ \text{s}$ is more than $0.1\ \text{s}$.

Practise with new numbers

Try it in Python

The program finds the echo time for walls at several distances.

Remember these

• Sound is reflected by hard surfaces; an echo is a reflected sound.
• Echo time: $t = \dfrac{2d}{v}$; distance: $d = \dfrac{vt}{2}$.
• A separate echo needs at least $0.1\ \text{s}$, so a wall at least $17\ \text{m}$ away in air.
• Many reflections give reverberation; soft materials absorb sound.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A man hears the echo of his shout $3\ \text{s}$ later. How far is the cliff?

2. Why is an echo not heard in a small room?

3. Name one use of the reflection of sound.

4. Why do cinema halls have soft, rough walls?