Echo Time by Distance

Echo time and distance

When sound bounces off a wall it makes the trip there and back, so the distance is d = (v · t) / 2, with t standing for the round-trip time. Take an example at 20 °C, where v=343 m/s: a 0.3 s echo puts the wall at 0.3·343/2 ≈ 51.5 m. You'll only hear the echo as separate from the original sound if the delay runs greater than 50 ms, which is about the length of one spoken syllable and means the reflector has to be at least ~17 m off. Active ranging like sonar, radar leans on the same equation rearranged: t = 2d / v.

Applications

You'll find it behind fishing sonar and echo-sounders, which map ocean depth (bathymetry), and Doppler traffic radar, where range gets paired with a frequency shift to read speed. It also drives medical ultrasound, building images from the echoes that bounce off tissue, plus geophysical seismic reflection used in oil exploration. And there's bat echolocation, with chirps at 25-100 kHz that pin down insects mid-flight.

FAQ

Why divide by 2? Because the time you measure covers the full round trip, with the wave heading out to the obstacle and coming back. Halving it gives you the one-way distance.

What if it's underwater? Swap v for the local speed of sound in water, around ~1480 m/s, which shifts with temperature, salinity and depth. The geometry doesn't change at all.

What's the difference between echo and reverberation? An echo is a clear, delayed copy of the sound with a gap over >50 ms. Reverberation, on the other hand, is the dense smeared tail you get from a pile of short reflections running together.

Can I use this with light? You can, and that's exactly what lidar and radar do. The catch is that v becomes the speed of light (~3·10⁸ m/s), so now you're measuring time-of-flight in nanoseconds.