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( Beat (acoustics))
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. When tuning instruments that can produce sustained tones, beats can readily be recognized. Tuning two tones to a unison will present a strange effect when the two tones are close in pitch but not yet perfectly centered, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternatively interfere constructively and destructively. When the two tones gradually approach fusion, the beating slows down and disappears, giving way to full-bodied unison resonance. This phenomenon manifests acoustically. 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 each 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 (see List of trigonometric identities) that the successive values of maxima and minima form a wave whose frequency equals the difference between the two starting waves. Let's demonstrate the simplest case, between two sine waves of unit amplitude
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