Result

Beat frequency

f_{beat} = ∣ f_{1} - f_{2} ∣

Statement

The rate at which the combined amplitude of two close frequencies rises and falls.

Symbols and units

$f_{beat}$	beat frequency	Hz
$f_{1}, f_{2}$	the two source frequencies	Hz

When it applies

Two waves of nearly equal frequency, close enough that their difference is itself audible or observable as a slow modulation.

Don't use when

Only meaningful when the two frequencies are close enough that the difference itself is a slow, perceptible modulation — for very different frequencies there's no audible 'beat', just two distinct tones.

Derivation

Superposing two waves of nearly equal frequency produces a wave whose amplitude envelope oscillates at the difference between the two frequencies:

f_{beat} = ∣ f_{1} - f_{2} ∣

Watch out for

The beat frequency is the DIFFERENCE, not the average or sum, of the two frequencies — a frequent point of confusion.