Beat (acoustics)

In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume, the rate of which is the difference of the two frequencies.

With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies as in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get farther apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a combination tone is produced.

This phenomenon is best known in acoustics or music, though it can be found in any linear system:

"According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes".

If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant (as when a pure note is played), but change over time: when the two waves are nearly 180 degrees out of phase the maxima of one wave cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the perceived volume.

It can be proven (with the help of a sum-to-product trigonometric identity) that the sum of two unit-amplitude sine waves can be expressed as a carrier wave of frequency ⁠f₁ + f₂/2⁠ whose amplitude is modulated by an envelope wave of frequency ⁠f₁ - f₂/2⁠:

Because every other burst in the modulation pattern is inverted, each peak is replaced by a trough and vice versa. The envelope is perceived to have twice the frequency of the modulating cosine, which means the audible beat frequency (if it is in the audible range) is:

"Monaural beats are when there is only one tone that pulses on and off in a specific pattern. With only one tone (as opposed to two tones with binaural beats), your brain has a much easier time adjusting and there is no need to balance separate tones.