Beats are the rhythmic swelling and fading you hear when two tones close in pitch sound together — the basis for how musicians tune instruments by ear. This calculator finds the beat frequency and beat period from two known tones, or works backward to find an unknown tone's frequency from a reference pitch and the beats you hear.
How the Beat Frequency Calculator works
When two sound waves of slightly different frequency travel through the same medium, they add together by superposition. At moments when the waves are in phase, their amplitudes reinforce and the combined sound is loud; at moments when they're out of phase, they partially cancel and the sound is quiet. This alternation repeats at a rate equal to the absolute difference between the two source frequencies, f_beat = |f1 - f2| — a standard result from wave-interference physics (e.g. Halliday/Resnick, Serway). The beat period, the time between successive loud pulses, is simply the reciprocal, 1 / f_beat.
Inputs and what they mean
On the Beat Frequency tab, f1 and f2 are the two tones sounding simultaneously, in hertz — order doesn't matter since the formula uses an absolute difference. The Beat Period tab accepts a beat frequency directly, useful when you already know the beat rate (e.g. from a tuner readout) and just want the time between pulses. The Tuning tab flips the problem around: enter a known reference frequency and the beats per second you hear against an unfamiliar tone, and it returns the one or two frequencies the unknown tone could be.
Limits and edge cases
Beats are most audible when the two frequencies are close together — within roughly 15-20 Hz of each other for most listeners; wider gaps tend to be heard as two separate pitches rather than a single warbling tone. When f1 equals f2, the beat frequency is 0 Hz and the tones are perfectly in tune. On the Tuning tab, a beat count alone can't tell you whether the unknown tone sits above or below the reference — that's why both candidates are shown unless you specify a direction, which you'd typically determine by slightly detuning the reference and listening for whether the beats speed up or slow down.