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A rocket is moving at a speed of 200 m s...

A rocket is moving at a speed of `200 m s^(-1)` towards a stationary target. While moving, it emits a wave of frequency 1000 Hz. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate (1) the frequency of the sound as detected by the target and (2) the frequency of the echo as detected by the rocket.

Text Solution

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When source of sound (here rocket), moves to wards stationary listener (here target or detector), frequency of sound heard by the stationary listener (or frequency of sound detected by the detector) is suppose `f _(L).` Now accordinf to formula we have,

Substituting the values according to sign convention, we get,
`(f_(L))/(330+0) = (1000)/(330 -200)`
`implies f _(L) = (1000 xx 330)/(130) =2538.46 Hz`
When source of sound (here rocket), moves towards some wall from which sound is reflected in the form of echo which is detected by detector in the rocket, suppose with frequency `f _(L).` Now according to formula we have,

In case of echo, we can consider it as a sound coming from an imaginary source moving with a velocity opposite to velocity of original (real) source of sound. Moreover according to sign convention, velocity in a direction from listener (here detector) to imaginary source is to be taken positive and velocity of sound is always to be taken positive. Now substituting values in above equation,
`(f._(L))/(330 + 200) = (1000)/(330 -200)`
`implies f._(L) = (1000 xx 530)/(130) =4076.92Hz`
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