Question

A source of sound whose frequency is $1000 \,Hz$ is moving with a speed $33 \,m / s$. The waves reflected by a fixed obstacle are registered by a receiver that moves together with the source. The speed of the sound waves is $330\, m / s$, then the frequency registered by the receiver is

• A. 0.9 kHz
• B. 1.1 kHz
• C. 1.2 kHz
• D. 2.2 kHz

Answer 1

Answer: (C)

Frequency of reflected sound, $f_{1}=f\left(\frac{v}{v-v_{s}}\right)$
$=1000\left(\frac{330}{330-33}\right)=\frac{1000 \times 330}{297}$
Frequency observed by observer,
$f_{2}=f_{1}\left(\frac{v+v_{D}}{v}\right)=\frac{1000 \times 330}{297}\left(\frac{330+33}{330}\right)$
$=\frac{1000 \times 363}{297}=1.2 \times 1000=1.2\, kHz$