The driver of a car travelling with speed $30\text{ ms}^{-1}$ towards a hill sounds a horn of frequency…
The driver of a car travelling with speed $30\text{ ms}^{-1}$ towards a hill sounds a horn of frequency $600\text{ Hz}$. If the velocity of sound in air is $330\text{ ms}^{-1}$, the frequency of reflected sound as heard by driver is [AIIMS 2017]
(a) $550\text{ Hz}$
(b) $555.5\text{ Hz}$
(c) $720\text{ Hz}$
(d) $500\text{ Hz}$
Solution
When the sound is reflected from the cliff, it approaches the driver of the car. Therefore, the driver acts as an observer and both source (car) and observer are moving.
In this case, the apparent frequency heard by the driver (observer),
$f' = f \left(\frac{v + v_o}{v - v_o}\right)$
Given, $f = 600\text{ Hz}$, $v = 330\text{ ms}^{-1}$ and $v_o = 30\text{ ms}^{-1}$
$f' = 600 \left(\frac{330 + 30}{330 - 30}\right) = 720\text{ Hz}$