Question

A rocket is moving at a speed of $200m/s$ towards a stationary target. While moving it emits a wave of frequency $1000Hz$ . 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 $=330m/s$ )

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

Answer 1

Answer: (D)

Given, speed of rocket, $v_1=200m/s$
Frequency emitted by the rocket, $v_1=1000HZ$
Velocity of sound, $v_{sound}=330m/s$
In Ist case

Apply Doppler's effect in sound's equation
$v=\frac{v+u_0}{v-u_1}$
Putting values,
$v_1=\frac{330+0}{330-220}\times 1000$
$v_1=\frac{33}{13}\times 1000Hz\dots (i)$
This frequency is reflected back to the rocket
In IInd case

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 Eq. (i)]
$=\frac{53}{13}\times 1000=4076.92Hz$
Thus, the most appropriate option is (d)