Audibility
Simple Explanation
The human ear can only detect sound frequencies roughly between 20 Hz and 20000 Hz (20 kHz) — this range is called audibility. Sounds below 20 Hz are infrasound, and above 20 kHz are ultrasound, both inaudible to humans.
Why Do We Need It?
Audibility also explains why an echo needs a minimum distance to be perceived as a separate sound at all — the human ear needs a minimum time gap (about 0.1 s) between two sounds to tell them apart.
Formula
Minimum Distance for a Distinct Echo
d_min = (v × t_min) / 2
The human ear needs a minimum gap of about 0.1 s between two sounds to perceive them as separate — so a reflecting surface must be at least this far away for its echo to be heard as distinct from the original sound, rather than blending into it.
- d_min
- — minimum distance for a distinguishable echo, in metres (m)
- v
- — speed of sound in the medium, in metres per second (m/s)
- t_min
- — the minimum time gap the human ear can distinguish, about 0.1 s
When to use it: Whenever determining how far away a surface must be for a person to perceive a distinct echo, rather than the sound simply seeming prolonged.
Worked Example
Find the minimum distance for a distinct echo
Find the minimum distance a wall must be from a listener (in air, v=340 m/s) for its echo to be heard as distinct from the original sound.
Why Does This Work?
The ear (and brain) can only separate two sounds if they arrive with enough of a time gap between them — below about 0.1 s, the reflected sound arrives too soon after the original and the two blend into one prolonged sound instead of being perceived as an echo.
Real-Life Example
Why small rooms do not produce noticeable echoes
Speaking in a small room does not usually produce a distinct, separately-heard echo, while shouting in a large canyon does.
A small room's walls are far closer than the 17 m minimum distance needed for a distinct echo in air, so any reflected sound arrives too quickly to be heard as separate from the original — it just makes the room sound slightly "livelier" (reverberation) instead.
Practice
Find the minimum distance for a distinct echo in water (v=1500 m/s), using the same 0.1 s minimum time.
MediumCommon mistake
Assuming audibility (20 Hz–20 kHz) is the same thing as the minimum-echo-distance rule — audibility is about which FREQUENCIES the ear can detect at all, while the minimum echo distance is about the ear's ability to separate two sounds in TIME; both are limits of human hearing, but they describe different things.
Quick Review
- Human audible range: about 20 Hz to 20 kHz.
- d_min = (v × t_min)/2, with t_min≈0.1 s.
- Below d_min, a reflected sound blends into the original instead of being heard as a separate echo.