Sound

Beats

two close notes throb

Two notes close in frequency drift in and out of step, and their sum throbs in loudness at the difference of the two frequencies.

Example

Two notes close in frequency drift in and out of step, and their sum throbs in loudness at the difference of the two frequencies.

highlighted = computed this step

Two notes close in pitch

Play two notes whose frequencies are close — here 5 and 3 hertz. They drift in and out of step: sometimes the crests line up and add, sometimes they oppose and cancel, over and over.

fa=5 Hz,fb=3 Hzf_a = 5\ \text{Hz}, \quad f_b = 3\ \text{Hz}
Two close waves and their sum: a beat patternTwo waves of slightly different wavelength and, in purple, their sum, which swells and shrinks in a repeating envelope.sum

The loudness throbs at the difference

Where the two add you hear a loud swell; where they cancel, a moment of quiet. These throbs come at the beat frequency, the difference of the two: 5 minus 3 is 2 hertz — two loud swells every second. (The picture shows the pattern across space; the throb you HEAR is this pattern in time.)

fbeat=∣fa−fb∣=5−3=2 Hzf_{\text{beat}} = |f_a - f_b| = 5 - 3 = \hl{2}\ \text{Hz}
waves 5 Hz against 3 Hz gives a clean beat frequency of 2 Hz, with the sum drawn as the honest point-by-point combination.