Beats

When two sound waves of equal amplitude and slightly different frequencies interfere with each other, the displacement equation for the resultant wave at a particular position can be determined. Its intensity rises and falls alternately with time.

The total length of the time axis represents one second. When the two waves are in phase, their amplitudes add.

And, when the two waves are exactly out of phase, the total amplitude is zero.

This periodic variation in sound intensity with time forms beats.

The resultant wave looks like a single sinusoidal wave with varying amplitude, which goes through two maxima and two minima in one second. The frequency of this amplitude variation is two hertz.

The number of beats heard per second is called beat frequency and is equal to the difference in frequency of the sound waves.

The time interval between two successive beats is defined as the beat period, which is the inverse of the beat frequency.