A train moving at a speed of `220ms^-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 `330ms^(-1)`)

Options

A. 3000 Hz
B. 3500 Hz
C. 4000 Hz
D. 5000 Hz

Answer

D

Explanation

Listener, L is at rest, the frequency heard by L
`v' = ((upsilon - upsilon_(L))/(upsilon - upsilon_(S)))v = ((upsilon - 0)/(upsilon - upsilon_(S)))v`
`= ((330)/(330 - 220)) 1000`
v' = 3000 Hz
Thus, v' will behave as source for train
So, the frequency v'' is heard by driver of the train.
`v'' = ((upsilon - upsilon_(L))/(upsilon - upsilon_(S)))v'`
`= ((330 - (-220))/(330 - 0))3000 = 5000` Hz
(Listener is approaching towards the source so `upsilon_(L)` is negative)
v'' = 5000 Hz