Question Paper from: JEE Main 2021 - Paper 1

A vehicle moving with velocity v and releasing the sound of frequency 400 Hz. Listening to the reflected sound from a wall of frequency 500 Hz. Find the velocity of vehicle v in $km / h$ .

Correct Answer :

132

Solution:

Chapter Name: Waves

Difficulty Level: Moderate

The frequency received by the wall is $f_{1} = \frac{V _{s}}{V _{s} - V} f_{0}$

Reflected frequency received by man is $f_{2} = \frac{V _{s} + V}{V _{s}} f_{1}$

$\Rightarrow f_{2} = (\frac{V _{s} + V}{V _{s}}) (\frac{V _{s}}{V _{s} - V}) f_{0} \Rightarrow f_{2} = (\frac{V _{s} + V}{V _{s} - V}) f_{0}$

$\Rightarrow 500 = \frac{330 + V}{330 - V} 400$

$\Rightarrow v = \frac{330}{9} \times \frac{18}{5} = 132 km / h r$

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