Two steady tones, one pulse: hear acoustic beats
Two continuous tones can make a pulsing sound. Compare three clips, then discover what controls the speed of the beats.
A sound that seems to breathe
Play A, then B. A stays steady. B swells and fades. Yet we have added no percussion: B contains just two pure tones, each held at a constant frequency and amplitude apart from the very short fades at the ends.
Play one file at a time, at a low, comfortable volume. A speaker is enough: both tones are already mixed into one mono channel. You can also follow the entire experiment using the written map below.
A · The starting point
Transcript
From 0:00 to 0:06: one continuous 220 Hz pure tone, with no speech. Its amplitude stays constant between a 0.03-second fade-in and a fade-out of the same length. No slow beating is added.
B · The pulsing sound
Transcript
From 0:00 to 0:06: 220 Hz and 222 Hz pure tones overlap in one mono channel. Their sum has two regular swells per second, with dips between them. Interior envelope maxima are 0.5 seconds apart. Short fades soften the beginning and end. No speech or percussion.
Before you play C
In C, the first tone stays at 220 Hz, while the second changes from 222 to 224 Hz. What do you predict: slower, unchanged or faster pulsing? Listen, then compare B and C again. Focus on the speed of the swells, not which file seems loudest.
C · A slightly wider gap
Transcript
From 0:00 to 0:06: 220 Hz and 224 Hz pure tones overlap in one mono channel. Their sum has four regular swells per second. Interior envelope maxima are 0.25 seconds apart: twice as close together as in B. Short fades soften the beginning and end. No speech or percussion.
The answer: twice as fast
C has four beats per second, compared with two for B. For two pure tones with nearby frequencies, the beat frequency is the difference between their frequencies: 222 − 220 = 2 Hz; 224 − 220 = 4 Hz. Here, “2 Hz” or “4 Hz” describes the repeating swells, not a separate bass note.
One hertz means one cycle per second. The tones in B therefore oscillate 220 and 222 times per second. The 222 Hz tone gradually moves ahead: their oscillations reinforce, then cancel, then reinforce again. Each tone stays steady; their sum varies.
A contains a single tone. In B and C, the two tones have equal amplitudes. B and C keep the same settings except for the second tone’s frequency. All three files last six seconds. Their perceived loudness can differ: this is not a loudness test.
The map, with no listening required
To follow the mechanism, take one second from the middle of the file, away from the fades. The marks below represent envelope maxima: moments when the combined amplitude is greatest. They do not draw the hundreds of rapid oscillations of the tones.
One second between two markers
Time (s) B C
1.00 | |
1.25 |
1.50 | |
1.75 |
2.00 | |B: a 0.50-second gap. C: a 0.25-second gap. Both endpoints are shown: count the intervals, not all the marks, to get 2 or 4 beats per second.
Why does the sound dip between maxima?
In this model, both tones have the same amplitude. When their oscillations are exactly opposed, their sum momentarily cancels; then it grows again. This does not mean that each tone has stopped. If the amplitudes were different, cancellation would be incomplete.
The files are simple digital mixtures, not recordings of a room or an instrument. They isolate the phenomenon. A real sound can contain several frequencies and produce a more complicated result.
Your turn: closer or further apart?
Now imagine 220 Hz and 221 Hz. What would the beat rate be? What if the second tone moved down to 218 Hz instead? Do the subtraction before reading on.
Answers: one beat per second for 220 and 221 Hz; two for 220 and 218 Hz. Take the positive size of the gap. Hearing two beats per second alone therefore cannot tell you whether the second tone is above or below 220 Hz.
Return to B, then C: the essential change is a tiny gap between two frequencies. To hear the result, follow what the two tones do together.