When a train approaches a stationary observer, the apparent frequency of the whistle is `n'` and when the same train recedes away from the observer, the apparent frequency is `n"`. Then the apperent frquency `n` when the observer sitting in the train is :

Options

A. `n = (n' + n'')/(2)`
B. `n = sqrt(n'n'')`
C. `n = (2n'n'')/(n' + n'')`
D. `n = (2n'n'')/(n' - n'')`

Answer

C

Explanation

`n' = n.(v_("sound"))/(v_("sound") - v_("train")) rArr (n' - n)v_("sound") = n'v_("train")`
`n'' = n.(v_("sound"))/(v_("sound") + v_("train")) rArr (n - n'')v_("sound") = n'v_("train")`
`rArr ((n' - n)/(n - n'')) = (n')/(n'') rArr n'n'' - n n'' = n'n - n'n''`
`rArr 2n'n'' = (n' + n'')n rArr n = (2n'n'')/((n' + n''))`