Beats

Play a 440 Hz tuning fork next to a guitar string ringing at 444 Hz and you won't hear two separate pitches. You'll hear one pitch that throbs, getting louder and softer four times a second. That throb is a beat. It happens because the two sound waves are constantly drifting in and out of step. At one instant their crests line up and the waves add constructively, giving a loud moment. A fraction of a second later the crests have drifted apart enough that one wave's crest meets the other's trough, and they cancel, giving a quiet moment. This cycle of lining up and falling out of phase repeats steadily, and your ear hears it as a slow pulsing envelope riding on top of the steady pitch.

The rate of that pulsing, the beat frequency, is simply the absolute difference between the two source frequencies: f_beat = |f1 - f2|. A 440 Hz fork with a 444 Hz string gives beats at |444 - 440| = 4 Hz, meaning four loud-soft cycles every second. The closer the two frequencies get, the slower the drift in and out of phase, so the beat frequency shrinks toward zero. Musicians use this directly: as a guitarist tunes a string toward a reference pitch, the throbbing slows down, and when it vanishes entirely the string is in tune.

Beats sit alongside interference and standing waves in this unit because they're the same superposition idea applied in time instead of space. Where two-slit interference spreads constructive and destructive spots across a screen, beats spread them across moments, giving a direct, audible way to measure how close two frequencies really are.