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A rocket is movig at a speed of 200 m/s ...

A rocket is movig at a speed of 200 m/s 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 (a) the frequency of the sound as detected by the target and (b) the frequency of the echo as detected by the rocket.

Text Solution

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(a) Here, `upsilon_(0) = 0`
`upsilon_(s) = 200 m//s, upsilon = 330` m/s
As the speed of the source is comparable to that of the sound wave, the observed frequency is
`v. = v ((upsilon - upsilon_(0))/(upsilon - upsilon_(s))) = 1000 ((330 - 0)/(330 - 200))`
`= (1000 xx 330)/(130) = 2538.5` Hz
(b) Now, target is the source (source of echo) and the rocket.s detector is the observer. Therefore, the frequency of the echo as detected by the rocket is
`v.. = ((upsilon + upsilon_(0))/(upsilon - upsilon_(s))) xx v.`
Here, `upsilon_(0) = 200` m/s
`upsilon_(s) = 0`
`therefore" "v.. = (330 + 200)/(330 - 0) xx 2538.5`
`~~` 4077 Hz
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