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A train moving at a speed of 220 $ms^{-1}$ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is: (speed of sound in air is 330 $ms^{-1}$)
A
3000 Hz
B
3500 Hz
C
4000 Hz
D
5000 Hz
Detailed Solution
The train is both the moving source and, for the echo, the moving observer approaching the reflector.
$f' = f\left(\frac{v + v_o}{v - v_s}\right) = 1000\times\frac{330 + 220}{330 - 220}$
$= 1000\times\frac{550}{110} = 5000$ Hz
$f' = f\left(\frac{v + v_o}{v - v_s}\right) = 1000\times\frac{330 + 220}{330 - 220}$
$= 1000\times\frac{550}{110} = 5000$ Hz