A police car with a siren of frequency 8 kHz | vedclass

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(A) The frequency of the sound reflected by the building and heard by the driver is given by the Doppler effect formula for a moving source and a movi

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$8.50$

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(A) The frequency of the sound reflected by the building and heard by the driver is given by the Doppler effect formula for a moving source and a moving observer.Given:Frequency of source $f_0 = 8 \ kHz = 8000 \ Hz$Velocity of source (car) $v_s = 36 \ km/h = 36 	imes \frac{5}{18} \ m/s = 10 \ m/s$Velocity of observer (driver) $v_o = 10 \ m/s$Speed of sound $v = 320 \ m/s$First,the building acts as an observer receiving sound from the car:$f' = f_0 \left( \frac{v}{v - v_s} ight) = 8000 \left( \frac{320}{320 - 10} ight) = 8000 \left( \frac{320}{310} ight)$Then,the building acts as a source reflecting the sound to the driver:$f'' = f' \left( \frac{v + v_o}{v} ight) = 8000 \left( \frac{320}{310} ight) \left( \frac{320 + 10}{320} ight)$$f'' = 8000 \left( \frac{330}{310} ight) = 8000 	imes 1.0645 \approx 8516 \ Hz = 8.516 \ kHz \approx 8.50 \ kHz$.

$A$ police car with a siren of frequency $8 \ kHz$ is moving with uniform velocity $36 \ km/h$ 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 (in $kHz$)

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