Waves and sound · Process
Echoes, reflection and absorption
The same shout comes straight back at you off a cliff and vanishes without trace in a bedroom. Two things decide which happens: what the surface is made of, and how far away it is.
Start here
Shout at a cliff and count.
Stand a few hundred metres from a rock face on a still day and shout once. A moment later your own voice comes back at you, a little quieter and unmistakably yours. Shout the same word in a carpeted bedroom and nothing comes back at all.
You are 170 m from the cliff and the echo reaches you 1.0 s after you shout. How far has the sound travelled in that second?
The sound made two journeys of 170 m: out to the cliff, and back to you. So it covered 340 m in that second — which is exactly the speed of sound in air. The total path is always twice the distance to the surface, and forgetting to halve is the commonest way to get an echo question wrong.
Sound that meets a surface does one of three things, and usually all three at once. Some of it is reflected — sent back the way it came. Some of it is absorbed — its energy taken up by the material and turned into a tiny amount of heating. Some of it is transmitted, carrying on into and through the material.
An echo is reflected sound arriving back at you late enough to be heard as a separate sound. Two things have to be true. Enough of it has to come back: a hard, flat, heavy surface reflects most of what hits it, while something soft and open-textured absorbs most of it. And it has to take long enough: if the reflection returns within about a tenth of a second your ear runs it together with the original and hears one sound, a bit fuller. Since sound covers about 340 m every second, that tenth of a second means the surface has to be roughly 17 m away or more.
At the bench · one shout, one flat surface, a stopwatch
Move the wall. Change the wall.
Change a control to begin
One shout in still air, and a flat surface facing you. Set how far away it is, and set what it is made of.
Commit first. You move twice as far from the same rock face and shout again. What happens to the time before the echo returns?
170 m
What the surface is
Distance to the surface
—
in still air at about 340 m/s
Total path, out and back
—
Time before it returns
—
What you hear
—
The figure
Five surfaces, one shout each
What sends sound back is hard, flat and heavy. What absorbs it is soft and full of holes, so the air can be pushed into the gaps and rub its way to a stop. Both ends of the list are wanted by somebody: a swimming pool has the first problem and a recording booth is built to have the second.
Writing it down · the shape of this relationship
Total path = distance + distance
d · distance to the surface · m
s · total path, out and back · m
Worked example · one step at a time
A cliff echo comes back 2.0 s after you shout. In that time the sound covers 680 m. How far away is the cliff?
Step 0 of 5
Convert
680 m stays 680 m
The distance is already in metres and the answer is wanted in metres, so there is nothing to convert.
Formula
d = s ÷ 2
The shout goes out and comes back, so the total path is two equal helpings of the distance.
Insert
d = 680 m ÷ 2
The 680 m is the whole journey, out to the cliff and back — not the distance to the cliff.
Fine-tune
680 ÷ 2 = 340
Metres divided by a plain number leaves metres.
Answer
d = 340 m
Forgetting to halve is the commonest way to get this wrong.
Worked example · one step at a time
An echo returns after the sound has travelled 1.02 km. How far away is the wall?
Step 0 of 5
Convert
1.02 km × 1000 = 1020 m
The answer is wanted in metres, and a kilometre is a thousand of them.
Formula
d = s ÷ 2
Out and back, so the path is two equal helpings of the distance.
Insert
d = 1020 m ÷ 2
The converted total goes in. The 1.02 never does.
Fine-tune
1020 ÷ 2 = 510
Metres divided by a plain number leaves metres.
Answer
d = 510 m
Halve 1.02 instead and the answer comes out 0.51 m — half a metre from a wall you shouted at.
Your turn · the same five steps
Your surface is 170 m away.
Write all five lines before you check. The distance is the one your own bench is showing.
The five lines, marked
Convert
the round trip is already in metres
The bench gives the whole path in metres and the answer is wanted in metres, so there is nothing to convert.
Formula
s = d + d
Two equal parts, out and back, make the whole path.
Insert
s = 170 m + 170 m
Both parts are the distance to the surface, which your slider sets.
Fine-tune
170 + 170 = 340
Metres added to metres leave metres.
Answer
s = 340 m
At about 340 m/s that takes 1.00 s, which is what the stopwatch on the bench reads.
The five lines above give 340 m for a surface 170 m away.
A sonar ping covers 2.4 km on its round trip to the sea bed and back. How deep is the water?
This one needs the Convert line to do some work.
The five lines, marked
Convert
2.4 km × 1000 = 2400 m
The answer is wanted in metres, so multiply the kilometres by 1000.
Formula
d = s ÷ 2
Down and back, so the path is two equal helpings of the depth.
Insert
d = 2400 m ÷ 2
The converted total goes in. The 2.4 never does.
Fine-tune
2400 ÷ 2 = 1200
Metres divided by a plain number leaves metres.
Answer
d = 1200 m
Halve 2.4 instead and the sea bed comes out 1.2 m down.
The five lines give 1200 m. The whole question turned on the first one.
Key fact
An echo is sound reflected back and heard as a separate sound. It needs a surface that sends enough of it back — hard, flat and heavy rather than soft and open — and it needs the surface to be far enough away, roughly 17 m or more in air, so that the reflection arrives more than about a tenth of a second late. The sound travels out and back, so the total path is twice the distance to the surface.
Think again
“An echo is a new sound the wall makes.”
The wall makes nothing. Your shout arrives, pushes on the surface, and most of it is sent straight back the way it came — which is why an echo is recognisably your own voice, your own words, in your own accent, and why it is a little quieter rather than a little different. A wall that made sounds of its own would be a very odd wall, and it would still be making them when you were silent.
“Soft materials stop sound travelling.”
Soft materials absorb sound, which is not the same as stopping it. Absorbing means the energy is taken up by the material and ends as a very small amount of heating; the sound stops existing rather than being turned back. Blocking is a different job and is done by mass, not softness: a thin foam panel kills an echo beautifully and does almost nothing to stop your neighbour hearing the television, while a solid brick wall does the opposite. A recording studio needs both, and uses different materials for each.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
You shout at a cliff and the echo returns 3.0 s later. Sound travels at about 340 m/s in air. How far away is the cliff?
Rung 2 · The one that catches people
A bedroom with a carpet, curtains and a bed gives no echo at all. Which statement is right?
Rung 3 · Explain
A school sports hall with bare brick walls and a hard floor is so echoey that announcements are hard to make out. Explain why, and describe one change that would fix it and why it would work.
Rung 4 · Take it somewhere new
A ship measures the depth of the sea by sending a pulse of sound straight down and timing what comes back. The pulse returns after 0.40 s, and sound travels at about 1500 m/s in sea water. Work out the depth, and say why the answer would be wrong if you forgot that the pulse makes two journeys.
Key note
Sound meeting a surface is partly reflected, partly absorbed and partly transmitted. An echo is reflected sound heard as a separate sound, and it needs both a surface that sends enough back — hard, flat and heavy rather than soft and open — and a distance of roughly 17 m or more, so the reflection arrives more than about a tenth of a second late. The sound travels out and back, so the total path is twice the distance to the surface.
Going further
Timing an echo is how a great deal of the world gets measured. A ship's echo sounder pings the sea bed and halves the answer; a bat does the same thing in air, fast enough to catch a moth in flight; an ultrasound scanner reads the reflections from the boundaries inside a body. Every one of them has to halve, and every one of them has to know the speed of sound in the material it is looking through — which is why a scanner set up for soft tissue would misplace everything if it were used on bone.
Designing a room for sound is a balancing act rather than a hunt for silence. A concert hall with no reflections at all sounds dead and lifeless, and musicians hate it; a hall with too many sounds like a swimming pool. Architects aim for a reverberation time — how long a sound takes to die away — of roughly two seconds for an orchestra, under a second for speech, and they get there by choosing how much of each surface is hard and how much is soft. Nothing about it stops sound reaching the audience; it only controls how much of it arrives late.
Before this lesson
Connects to
At GCSE this becomes
- Reverberation time, ultrasound and echo sounding calculations, and the reflection, absorption and transmission of waves at a boundary.
Where to next
Ask Mr Badmus AI
Got an echo to time, or a room that sounds wrong?
The bench is a teaching model. The percentages of sound sent back are round teaching figures for a typical surface of each kind: real reflection depends strongly on the frequency of the sound and on the angle it arrives at, and a curtain that absorbs a high note well may do almost nothing to a low one. The 15% below which no separate echo is heard, and the tenth of a second inside which your ear runs two sounds together, are both approximate thresholds fixed here so that the states can be reached and compared. The speed of sound is taken as about 340 m/s, its value in air at around 20 degrees Celsius. The surface is treated as flat and facing you squarely, with no sound lost on the way there and back; over hundreds of metres a real shout both spreads and is absorbed by the air.
Lesson content © MrBadmusAI.