JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Waves & Sound

A person driving car at a constant speed of

15 m / s

is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of horn is

____

Hz.
(Given : Speed of sound :

330 m / s

)

Answer: 420

Solution

This is a Doppler effect problem where the car acts as both source and observer. The reflected sound from the wall has frequency

f^{'} = (\frac{v + v _{c}}{v - v _{c}}) f_{0}

, where

v = 330

m/s is the speed of sound,

v_{c} = 15

m/s is the car's speed, and

f_{0}

is the horn's frequency. The change in frequency is

Δ f = f^{'} - f_{0} = 40

Hz. Substituting:

(\frac{345}{315}) f_{0} - f_{0} = 40

, which gives

\frac{30}{315} f_{0} = 40

. Solving:

f_{0} = \frac{40 \times 315}{30} = 420

Hz.

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Integer answer

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