Two tuning forks with natural frequencies 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards the observer at the same speed. The observer hears beats offrequency 3 ~Hz . Find the speed of the tuning forks.

Step-by-step solution

Let v= speed of sound and v_ S = speed of tuning forks. Apparent frequency of fork moving towards the observer is n ₁= ( v v - v _ s ) n Apparent frequency of the fork moving away from the observer is n ₂= ( v v + v _ s ) n If f is the number of beats heard per second. then f = n ₁- n ₂ array l f = ( v v - v _ s ) n - ( v v + v _ s ) n f = v ( v + v _ s )- v ( v - v _ s ) v ²- v _ s ² ( n ) 2 vv _ s n v ²- v _ s ² = f 2 ( v _ s v )= n = f . if v _ s < K v array v_ s = fv 2 n array l putting v =340 ~m / s , f =3, n