First slide

Doppler's effect

Question

Two sirens situated one kilometer apart are producing sound of frequency 330 Hz. An observer starts moving from one siren to the other with a speed of 2 m/s. If the speed of sound be 330 m/s, what will be the beat frequency heard by the observer

Moderate

A

8
B

4
C

6
D

1

Solution

Observer is moving away from siren 1 and towards the siren 2.
Hearing frequency of sound emitted by siren 1
$n_{1} = n (\frac{v - v_{0}}{v}) = 330 (\frac{330 - 2}{330}) = 328 Hz$
Hearing frequency of sound emitted by siren 2
$n_{2} = n (\frac{v + v_{0}}{v}) = 330 (\frac{330 + 2}{330}) = 332 Hz$
Hence, beat frequency $= n_{2} - n_{1} = 332 - 328 = 4 .$

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