A police car with a siren of frequency 8 , kH | vedclass

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(A) The frequency heard by the driver is due to the reflection of sound from the building. The building acts as a stationary source reflecting the sou

Vedclass · Accepted Answer

$8.50$

Vedclass · Answer

(A) The frequency heard by the driver is due to the reflection of sound from the building. The building acts as a stationary source reflecting the sound.First,the frequency $f_b$ received by the building is given by the Doppler effect formula for a moving source and stationary observer: $f_b = f \left( \frac{v}{v - v_s} ight)$,where $v = 320 \, m/s$,$v_s = 36 \, km/hr = 10 \, m/s$,and $f = 8 \, kHz$.$f_b = 8 \left( \frac{320}{320 - 10} ight) = 8 \left( \frac{320}{310} ight) \, kHz$.Now,the building acts as a stationary source reflecting this frequency $f_b$ back to the moving car (observer). The frequency $f'$ heard by the driver is: $f' = f_b \left( \frac{v + v_o}{v} ight)$,where $v_o = 10 \, m/s$.$f' = \left( 8 	imes \frac{320}{310} ight) 	imes \left( \frac{320 + 10}{320} ight) = 8 	imes \frac{330}{310} \approx 8.516 \, kHz$.Rounding to the nearest provided option,the correct frequency is $8.50 \, kHz$.

$A$ 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 .... $kHz$.

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