# Beats

Superposition of waves of same frequency propagating in the same direction produces interference. The outcome of superposition of waves of nearly the same frequency is beats.

### Production of Beats

Suppose there are two tuning forks A and B of frequencies N and N + n respectively. The value of n is smaller than 10. In one second, A completes N vibrations but B completes N + n vibrations. B completes n more vibrations in one second than the tuning fork A.

In other words, B gains n vibrations over A in 1 s and hence it gains 1 vibration in (1/n) s and half vibration over A in (1/2n) s.

Suppose at t = 0 (initially), both the tuning forks were vibrating in the same phase. Then, after (1/2n) s, B will gain half vibration over A. Thus after (1/2n) s, it will vibrate in opposite phase. If A sends a wave of compression then B sends a wave of rarefaction to the observer. The resultant intensity received by the ear would be zero.

After (1/n) s, B would gain one complete vibration. If now A sends a wave of compression, B too would send a wave of compression to the observer. The intensity observed would become maximum. After (3/2n) s, the two forks again vibrate in the opposite phase and hence the intensity would again become minimum. This process would continue.

The observer would hear 1 beat in (1/n) s, and hence n beats in one second. Thus, the number of beats heard in one second equals the difference in the frequencies of the two tuning forks.

If more than 10 beats are produced in one second, the beats are not heard as separate. The beat frequency is n and beat period is 1/n.