Two slightly different frequencies overlap — and you hear a slow oscillation in volume. Beat frequency = |f₁ − f₂|.
Graph
y = sin(10 · x) + sin(11 · x)
Superposition — add two waves, watch the sum
close frequencies → beats: the sum swells and fades |f₁ − f₂| = 1 time per cycle (dashed envelope)
Beat frequency
Two tones close in pitch interfere — the loudness swells and fades f_beat times per second. The waveform above shows the slow envelope wrapping the fast wiggle.
Your turn
You play a 440 Hz tuning fork next to a slightly flat A string and hear 3 beats per second. What two frequencies could the string be?
Piano tuners and orchestras tune *by* beats: adjust until the wah-wah slows to nothing — then the notes are matched exactly.
Musicians tune by reducing beats. When the beats vanish, the notes match.