JEE Advanced · 2011 · 10 Apr 2011 · Paper 1 · Waves & Sound

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A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is

320 m / s

. The frequency of the siren heard by the car driver is

(A)8.50 kHz✓ Correct
(B)8.25 kHz
(C)7.75 kHz
(D)7.50 kHz

Answer: (A)

Solution

The car driver hears sound from two sources: the direct sound from the siren and the reflected sound from the building. For the reflected sound, the building acts as a stationary observer receiving frequency

f^{'} = \frac{v}{v - v _{s}} f_{0}

, and then as a stationary source reflecting back to the moving car (now acting as a moving observer). The net frequency heard is:

f = \frac{v + v _{s}}{v - v _{s}} f_{0} = \frac{320 + 10}{320 - 10} \times 8 \times 1 0^{3} = \frac{330}{310} \times 8000 = 8.516 kHz \approx 8.50 kHz

where

v_{s} = 36 km/hr = 10 m/s

JEE Advanced · 2011 · 10 Apr 2011 · Paper 1 · Single correct option

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JEE Advanced · 2011 · 10 Apr 2011 · Paper 1 · Waves & Sound

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