Stand at the mouth of a cave, or across a valley from a big cliff, and shout your name. A moment later your name comes flying back at you out of the rock — "…name… name…" You didn't shout twice. Nobody in the cliff shouted back. So what happened?

Sound is a wave, and when a wave runs into a hard, flat surface it bounces off — it reflects, just like a ball thrown at a wall. The reflected sound racing back to your ears is an echo. This page takes that one simple idea — sound reflects — and shows how it becomes a ruler for measuring distances you could never reach with a tape measure: the depth of the ocean, the crack hidden inside a steel bridge, even a baby before it is born.

An echo is a stopwatch for distance

Here is the clever part. Sound travels at a known, steady speed — about 340\ \text{m/s} in air (you met this on wave speed). So if you can time how long an echo takes to come back, you can work out how far away the reflecting surface is. Distance is just speed multiplied by time:

But there is a catch that trips almost everyone up. The sound doesn't travel to the wall and stop — it travels all the way there and all the way back before you hear it. The time t you measured is the time for the round trip, which is twice the distance to the wall. So to find the distance to the wall itself, you must halve it:

Worked example — how far is the cliff? You clap, and the echo from a cliff returns 2\ \text{s} later. Sound travels at 340\ \text{m/s}. How far away is the cliff?

The sound actually flew 680\ \text{m} in total (there and back) — but the cliff is 340\ \text{m} away. Forget the \div 2 and you'd say the cliff was twice as far as it really is.

Watch the pulse go and come back

Below, a source on the left sends out a short pulse of sound. It races across to the wall, reflects, and comes racing back. Drag the second slider to send the pulse on its round trip and watch the running total. Then move the wall further away and send it again — the echo takes longer to return, because the sound has further to travel. The readout shows the round-trip time t and the distance the formula recovers, d = \tfrac{v\,t}{2}.

Notice the pulse crosses the same gap twice. That is the whole reason for the \div 2: the clock runs for both legs of the journey, so half the timed distance is the one-way distance to the wall.

Ultrasound: sound too high to hear

Your ears can only hear sounds within a certain range of frequencies — from about 20\ \text{Hz} (a very low rumble) up to about 20\,000\ \text{Hz} = 20\ \text{kHz} (a very high whistle). Sound with a frequency above 20\ \text{kHz} — too high for any human to hear — is called ultrasound.

Ultrasound is still just sound: a wave of vibrations passed along through a material, exactly like the sound you can hear. It is not light, not radio, not X-rays — it carries no radiation and needs a material to travel through. What makes it so useful is that, like all sound, it reflects at a boundary between two different materials — where soft tissue meets bone, where metal meets an air-filled crack, where water meets the seabed. Send a pulse of ultrasound into an object, time the reflections that bounce back from each boundary inside it, and those echo times reveal what is hidden inside — without ever cutting it open.

Where echoes and ultrasound are used

The same trick — send a pulse, time the echo, compute the distance with d = \tfrac{v t}{2} — turns up everywhere:

• Prenatal scans (sonograms). A probe sends ultrasound pulses into the body; the echoes from the boundaries inside are timed and turned into a picture of the baby. Because it is just sound — no ionising radiation like an X-ray — it is considered safe for the unborn baby.
• Medical imaging generally. The same machines image a beating heart, muscles, blood flow and organs, all from reflected ultrasound.
• Industrial flaw detection. Fire ultrasound into a metal casting, an aircraft wing or a weld: an unseen crack or air bubble inside is a boundary, so it sends back an early echo — revealing the flaw before the part fails.
• Sonar and echo-sounding. A ship pings a pulse down into the water and times the echo from the seabed to measure the depth, or spots shoals of fish and submarines the same way.
• Echolocation in animals. Bats and dolphins do it naturally — squeaking or clicking and listening for the echoes to "see" their world in the dark or the murk.

More worked examples

Example 1 — the depth of the sea. A ship's echo-sounder sends a pulse straight down and the echo returns from the seabed after 0.4\ \text{s}. Sound travels through seawater at v = 1500\ \text{m/s}. How deep is the water?

The seabed is 300\ \text{m} below the ship.

Example 2 — timing the echo the other way round. A wall is 85\ \text{m} away and sound travels at 340\ \text{m/s}. How long after you clap will you hear the echo? Here the sound covers the distance twice, so rearrange the formula for t:

Half a second later, the echo arrives.

Example 3 — a flaw inside metal. An ultrasound pulse fired into a steel block (where sound travels at v = 6000\ \text{m/s}) reflects off a hidden crack and returns in 0.0002\ \text{s}. How far below the surface is the crack?

The crack lies 0.6\ \text{m} in from the surface.