JEE Advance - Physics (2011 - Paper 1 Offline - No. 8)

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
8.50 kHz
8.25 kHz
7.75 kHz
7.50 kHz

Explanation

u = 36 km h$$-$$1 = 10 ms$$-$$1,

$$v$$ = 320 ms$$-$$1, $$\nu $$ = 8 kHz

The sound reflected from the building may be imagined to be coming from the mirror image. The driver is approaching the image-source which is also approaching him with the same speed. Hence the frequency of sound heard by the driver is

$$\nu $$' = $$\nu $$ $$\left( {{{v + u} \over {v - u}}} \right)$$

= 8 kHz $$\times$$ $$\left( {{{320 + 10} \over {320 - 10}}} \right)$$ = 8.5 kHz

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