Question

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

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

Answer 1

The correct option is C $5000Hz$

As the source (i.e rocket) is moving toward the stationary target, therefore the frequency of sound detected by the target is
${\upsilon }^{\prime }=\frac{{\upsilon }_0\nu }{\nu -{\nu }_s}=\frac{1000\times 330}{330-220}=\frac{1000\times 330}{110}=3000Hz$
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 \acute{\upsilon}. Hence, the frequency of the echo detected by the rocket is

$\upsilon "=\frac{{\upsilon }^{\prime }(\nu +{\nu }_O)}{\nu }=\frac{3000(330+220)}{330}=5000Hz$