How this calculator works
Two similar tones alternately reinforce and cancel. Equal-amplitude sine waves produce an envelope whose loudness maxima recur at the frequency difference. Recovering a tone has two possible branches, so choose whether the missing tone is higher or lower. Widely separated frequencies still have a mathematical difference but may not sound like slow beats.
Formula
fb = |f1-f2|; fmean = (f1+f2)/2; y(t) = cos(2 pi f1 t)+cos(2 pi f2 t). Beat period = 1/fb when fb > 0.
Worked example
Tones at 440 Hz and 444 Hz give four beats per second and a beat period of 0.25 s. A tone 5 Hz below 440 Hz is 435 Hz.
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Frequently asked questions
Why are there two inverse answers?
A frequency difference alone cannot tell which tone is higher.
What happens when frequencies match?
The beat frequency is zero and there is no finite beat period.
Does the graph show sound pressure in pascals?
No. It uses two unit-amplitude tones to show interference, with no calibrated sound level.