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

Answer

C

Explanation

As the source (i.e rocket) is moving toward the stationary target, therefore the frequency of sound detected by the target is
`upsilon'=(upsilon_(0)v)/(v-v_(s))=(1000xx330)/(330-220)=(1000xx330)/110=3000Hz`
Now the target is the source (as it is the source of echo) and the rocket's detector is the observer who intercepts the echo of frequency `upsilon'`. Hence, the frequency of the echo detected by the rocket is
`upsilon''=(upsilon'(v+v_(O)))/v=(3000(330+220))/330=5000 Hz`