Two tuning forks with natural frequencies of `340 Hz` each move relative to a stationary observer. One fork moves away form 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.

Explanation

As observer is at rest-
`n'=n ((V)/(V = V_(s))),n_(1) = n((V)/(V - U))`
and `n_(2) n((V)/(V+U))`
Now as beat frequency is 3 Hz so `n1 and n2` are very close which is possible only when:
`U lt lt V ` . so using Binomial theorem.
`n_(1) = n (1 - (U)/(V))^(-1) = n (1 + (U)/(V))`
and ` n_(2) = n (1 + (U)/(V))^(-1) = n (1 - (U)/(V))^(-1)`
So beat frequency `Delta n= n_(1) n_(2) = n ((2U)/(V))`
`rArr U = (V)/(2) ((Deltan)/(n))`
`(330)/(2) ((3)/(340)) = 1.45 m//s `