Question

A rocket is moving at a speed of 220 $ms^{- 1}$ towards a stationary target, emits a sound of frequency 1000 Hz. Some of the sound reaching the target gets reflected back to the rocket as an echo. The frequency of the echo as detected by the rocket is. (Take velocity of sound = 330 $ms^{- 1}$)

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

Answer 1

Answer: (D)

3000 Hz

Answer 2

As the source (i.e, rocket) is moving towards the stationary target, therefore the frequency of sound detected by the target is

$\upsilon` = \frac{\upsilon_{0}v}{v - v_{s}}$

$= \frac{1000 \times 330}{330 - 220} = \frac{1000 \times 330}{110}3000Hz$

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

$\upsilon'' = \frac{\upsilon'(v + v_{O})}{v}$

$= \frac{3000(330 + 220)}{330} = 5000Hz$