Question

Two tuning forks with natural frequencies of 340 Hz each move relative to a stationary observer. One fork moves away from the observer while the other moves towards him at the same speed. The observer hears beats of frequency 3 Hz. Find the speed of the tuning fork. Speed of sound in air = 340 m/s.

Answer 1

Let v_s be the speed of source and # be that of the sound waves. Let v be the frequency of the tuning fork. If v' is its apparent frequency when it moves towards the stationary observer

Applying binomial theorem (as v_s /v < 1), we get

If v’’ is the apparent frequency of the tuning fork when it moves away from the stationary source, 

Applying binomial theorem (since v_s /v< 1), we get