Last updated: 2026-06-15

Beat Frequency

Play two notes that are almost the same pitch and you hear something neither note makes alone: a slow throbbing, a rise and fall in loudness. That throb is the beat, and how fast it pulses is the beat frequency. It is the simplest audible sign of wave interference, and it is the basis of how musicians tune by ear.

Where beats come from

Two sound waves of slightly different frequencies slowly slip in and out of step. When their crests line up they reinforce and the sound is loud; a moment later, crest meets trough, they cancel, and the sound dips. The loud-soft cycle repeats at a rate equal to the difference between the two frequencies:

The absolute value is there because a beat rate is never negative — only the size of the gap between the pitches matters, not which one is higher.

Worked example

A tuning fork at $f_1 = 440\ \text{Hz}$ sounded against a string at $f_2 = 443\ \text{Hz}$:

You would hear three swells per second. The beat period — the time between loud points — is the reciprocal,

Tuning by beats

This is why beats are a tuner's best friend. As you bring a string toward a reference pitch, the beats slow down; the closer the match, the longer the gap between throbs. When the beats vanish altogether, the two frequencies are identical and the note is in tune. Listening for a slow beat is far more precise than trying to judge two pitches against each other directly.

Beyond music

The same arithmetic appears wherever two close frequencies mix. Radio receivers deliberately beat an incoming signal against a local oscillator to shift it to a fixed intermediate frequency. Vibration engineers hear beats when two machines run at nearly the same speed. And piano tuners stretch certain intervals by setting a deliberate, steady beat rate rather than eliminating beats entirely.