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.

Answer

A

Explanation

The apparent frequency from tuning fork `T_(1)` as heard by the observer will be

`v_(1) = (c )/(c - v) xx v` …(i)
where `c = velocity of sound`
`v = velocity of turning fork`
The apparent frequency from tuning fork `T_(2)` as heard by the observer will be
`v_(2) = (c )/(c + v) xx v` ...(ii) Given `v_(1) - v_(2) = 3`
:. `c xx v [(1)/(c - v) - (1)/(c + v)] = 3` or, `3 = (c xx v xx 2v)/(c^(2) - v^(2))`
Since, `v lt lt c` :. `3 = (c xx v xx 2v)/(c^(2)`
:. `v = (3 xx 340 xx 340)/(340 xx 340 xx 2) = 1.5 m//s`