Beats, periodic changes in the amplitude of an oscillation that arise when two harmonic oscillations of close frequency are added. Beats arise because the phase difference between two oscillations of different frequency changes all the time, so that at some moment the two oscillations are in phase, after some time in antiphase, then in phase again, and so on. If A1 and A2 are the amplitudes of the two superposed oscillations — then, when the phases of the oscillations are the same, the amplitude of the resultant oscillation reaches its greatest value A1+A2, and when the phases of the oscillations are opposite, the amplitude of the resultant oscillation falls to its smallest value A1-A2.
Beats arising from the superposition of two oscillations of close frequency; T — the period of the beats.
In the simplest case, when the amplitudes of the two oscillations are equal, their sum reaches the value 2A when the phases of the oscillations are the same and falls to zero when they are opposite in phase (Fig.).
The result of the superposition of the oscillations can be written in the form:
where ω1 and ω2 are the corresponding angular frequencies of the two superposed harmonic oscillations. If ω1 and ω2 differ little, then in expression (1) the quantity
can be regarded as a slowly varying amplitude (the envelope) of the oscillation
The angular frequency Ω=ω1-ω2 is called the angular frequency of the beats. Thus, beats are one variety of amplitude-modulated oscillations (see Modulation of oscillations). As the frequencies ω1 and ω2 draw closer together the beat frequency decreases, vanishing as ω1→ω2 (“zero” beats). Determining the frequency of the beat tone between the oscillation being measured and a reference oscillation is one of the most accurate methods of comparing a measured quantity with a standard, and is widely used in practice; the beat method is used to measure frequencies, capacitance and inductance, to tune musical instruments, in the analysis of auditory perception, and so on.