Question

A rocket is moving 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. The frequency of the echo as detected by the rocket is (velocity of sound $= 330 \,m/s$ )

• A. $1000\, Hz$
• B. $1580\, Hz$
• C. $2540\, Hz$
• D. $4080\, Hz$

Answer 1

Answer: (D)

$4080\, Hz$

Answer 2

Given, speed of rocket, $v_{1}=200 \, m/s$
Frequency emitted by the rocket, $v_{1}=1000\,HZ$
Velocity of sound, $v_{sound}=330\, m/s$

Apply Doppler's effect in sound's equation
$v=\frac{v+u_{0}}{v-u_{1}}$
Putting values,
$v_{1}=\frac{330+0}{330-220} \times 1000$
$v_{1}=\frac{33}{13} \times 1000\,Hz \dots(i)$
This frequency is reflected back to the rocket

Apply Doppler's effect in sound's equation
$v_{2}=\frac{330+200}{300}v_{1}$
$=\frac{530}{330}\times \frac{33}{13}\times 1000$ [from E (i)]
$=\frac{53}{13}\times1000=4076.92\,Hz$
Thus, the most appropriate option is (d)