Echo
Simple Explanation
An echo is a reflected sound wave, heard after the original sound bounces off a distant surface (like a cliff or wall) and returns. Since the sound travels the distance twice (out and back), d=vt/2.
Why Do We Need It?
Echoes are a direct, measurable demonstration that sound is a wave that reflects — and the same principle (timing a reflected wave) underlies sonar, radar, and medical ultrasound imaging.
See It
A source/listener on the left and a wall on the right, with an arrow showing the sound traveling out to the wall labelled d, and a second arrow below showing the echo returning
Formula
Distance to a Reflecting Surface (from an Echo)
d = vt / 2
The distance to a wall or other reflecting surface, found from the total round-trip time for a sound to travel out, reflect, and return — divided by 2 since the sound covers the distance twice.
- d
- — distance to the reflecting surface, in metres (m)
- v
- — speed of sound in the medium, in metres per second (m/s)
- t
- — total round-trip time from the sound being made to the echo being heard, in seconds (s)
When to use it: Whenever the distance to a reflecting surface needs to be found from the time it takes to hear an echo.
Worked Example
Find the distance to a wall using an echo
A person shouts toward a cliff and hears the echo 0.6 s later. If sound travels at 340 m/s, find the distance to the cliff.
Why Does This Work?
The measured time t covers the sound's ENTIRE round trip — traveling out to the surface, then back to the listener — so the one-way distance is only half of vt, exactly what dividing by 2 accounts for.
Real-Life Example
Sonar depth-finding on a ship
A ship's sonar sends a sound pulse downward and measures how long it takes to hear the echo reflected off the ocean floor.
Using exactly d=vt/2 (with the speed of sound in water instead of air), sonar calculates the ocean depth directly from that round-trip timing.
Practice
A ship's sonar (v=1500 m/s in water) receives an echo 0.8 s after sending a pulse. Find the depth of the ocean floor.
MediumCommon mistake
Forgetting to divide by 2 — the measured time is for the ROUND trip, not the one-way distance, so skipping the ÷2 gives a distance twice as large as the true value.
Quick Review
- d = vt/2 — divide by 2 for the round trip.
- An echo is sound reflecting off a distant surface.
- The same timing principle underlies sonar and radar.