A train has just completed a U-curve in a trach which is a semi circle. The engine is at the forward end of the semi circular part of the trach while the last carriage is at the rear end of the semi circular track. The driver blows a whistle of frequency 200 Hz. Velocity of sound is `340(m)/(s)`. Then the apparent frequency as observed by a passenger in the middle of the train, when the speed of the train is 30 m/s, is

Options

A. 219 Hz
B. 188 Hz
C. 200 Hz
D. 181 Hz

Answer

C

Explanation

The Doppler formula holds for non collinear motion if `v_s` and `v_0` are taken to be the resolved component along the line of slight. In this case, we have `v_0=-v_tsin45^@=-(30)/(sqrt2)(m)/(s)`
`v_s=-v_tsin45^@=(30)/(sqrt2)(m)/(s)`
We have, `v=340(m)/(s)`,`n=200Hz` The apparent frequency `n'` is given by
`n'=n[(v-v_0)/(v-v_s)]=200[(340+((30)/(sqrt2)))/(340+((30)/(sqrt2)))]=200Hz`