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

Frequency received by observer `O` from `S_(1):`
`f_(1) = f((v)/(v - v_(s))) = (f_(v))/(v - u)`
Frequency receiver by observer `O` from `S_(2):`
`f_(2) = f((v)/(v + v_(s))) = (f_(v))/(v + u)`
`f_(1) - f_(2) = 3`
`(f_(v))/(v - u) - (f_(v))/(v + u) = 3`
`f_(v)[((v + u) - (v - u))/(v^(2) - u^(2))] = 3`
`(2 f v u)/(v^(2) - u^(2)) = 3`
Since frequency difference is very small i.e. `u lt lt v` i.e., `u^(2)` is negligible
`(2 f v u)/(v^(2)) = 3 rArr (2 f u)/(v) = 3`
`u = (3 v)/(2 f) = (3 xx 340)/(2 xx 340) = 1.5 m//s`