Two sine waves of close but different frequencies produce audible beats at a rate equal to their frequency difference

When two sine waves of frequencies f₁ and f₂ are sounded simultaneously, their amplitudes add and subtract periodically, creating an envelope that fluctuates at rate |f₁ - f₂| Hz. This amplitude modulation is heard as beats — a periodic waxing and waning in loudness. If f₁ = 220 Hz and f₂ = 221 Hz, the beat rate is 1 Hz (one beat per second). If f₂ = 225 Hz, the beat rate is 5 Hz (five beats per second). As the frequency difference grows, beats first become faster and more unpleasant (roughness), then the two tones resolve into separate pitches. Beats are used in instrument tuning: two strings tuned to the same pitch produce no beats; beats disappear when tuning is exact.

Examples

Tuning a piano by ear: strike two strings for the same note; if you hear slow beating, one string is slightly off. Adjust until beats disappear. Two oboes warming up at slightly different pitches produce slow beats. Detuned oscillators in a synthesizer create chorus-like beating.

Assessment

Two sine waves sound together at 330 Hz and 336 Hz. (a) What is the beat rate? (b) If the 336 Hz wave is retuned to 330 Hz, what happens to the beats? (c) Describe the perceptual transition as the frequency difference increases from 0 to 50 Hz.