Question

The driver of a car travelling with speed $30\, ms ^{-1}$ towards a hill sounds a horn of frequency $600\, Hz$. If the velocity of sound in air is $330\, ms ^{-1}$, the frequency of reflected sound as heard by driver is

• A. 550 Hz
• B. 555.5 Hz
• C. 720 Hz
• D. 500 Hz

Answer 1

Answer: (C)

When the sound is reflected from the cliff, it approaches the driver of the car. Therefore, the driver acts as an observer and both sources (car) and observer are moving.
In this case, the apparent frequency heard by the driver (observer),
$f'=f\left(\frac{v+v_{0}}{v-v_{0}}\right)$
Given, $f=600\, Hz$
$v =330\, ms ^{-1}$
$v_{0} =30\, ms ^{-1}$
$f'=600\left(\frac{330+30}{330-30}\right)=720\, Hz$