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Question

# A police car with a siren of frequency 9 kHz is moving with uniform velocity 75 km/hr towards a tall building which reflect the sound wave. The speed of sound in air is 340 m/s. The frequency of siren heard by the car driver is

A
8 kHz
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B
10 kHz
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C
2 kHz
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D
14 kHz
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Solution

## The correct option is B 10 kHzVelocity of sound (v)=340 m/s Velocity of car (vs)=75×10003600=20.83≈21 m/s Frequency generated by given car siren (fo)=9 kHz Let fb be the frequency observed by building, Velocity of observer (vo)=0 m/s Applying Doppler effect, fb=fo(v±vov±vs) ⇒fb=fo(vv−vs)=9×340340−21=9×340319 kHz Frequency of reflected wave by building, fb=9×340319 kHz Now let fapp be the frequency heard by police or also known as an apparent frequency. Doppler's effect for given value, Here velocity of source (vs)=0 Velocity of observer (vo)=21 m/s fapp=fb(v±vov±vs)fapp=9×340319×340+21340 fapp=10.184 kHz≈10 kHz Caution: Be careful, when taking the sign convention in Doppler effect.

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