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 of frequency 3 Hz. Find the speed of the tuning forks (speed of sound is `340(m)/(s)`).

Explanation

As observer is at rest, `f_(Ap) = f[(v)/(v pm V_S)]`
If speed of tuning fork is `u, f_A = f [v/(v-u)]` while `f_R =f[v/(v +u)]`
Now as beat frequency is 3Hz, so `f_A and f_R` are very close which is possible onlyif `u lt lt v`. So using binomial theorem, `f_A = f [1-u/v]^(-1) = f[1 +u/v]`
and `f_R = f[1+u/v]^(-1) =f[1 - u/v]` So beat frequency
`Deltaf = f_A - f_R = f [ (2u)/(v)]`
`i.e., u =v/2 [(Deltaf)/(f)] =340/2 [3/(340)] = 1.5 m//s`