What are beats? Give the theory of beats.

Explanation

The phenomenon of waxing and waning of sound as a result of superposition of two progressive waves differing in their frequencies slightly `( le 10 Hz)` is known as beats (audible).
Let `y_1=A sin omega_1 t and y_2 sin omega_2 t` represent two progressive waves travelling in the same. direction and superpose with each other.
`y=y_1+y_2=A(sin omega_1 t+sin omega_2 t)`
i.e., `y=2A sin.((omega_1+omega_2))/(2) t cos.((omega_1+omega_2))/(2) t`
i.e., `omega=(omega_1+omega_2)/(2)`
and `omega_b=omega_2 or f_b=f_1-f_2` where `'f_b'` is known as the beat frequency and `t_b=(1)/(f_b)=(1)/(f_1-f_2)` as the beat period.