A vehicle sounding a whistle of frequency 256 | vedclass

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(D) The source (whistle) and the observer (person in the vehicle) are moving together with the same velocity $v_s = 10 \,ms^{-1}$ towards the hill.The

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$16$

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(D) The source (whistle) and the observer (person in the vehicle) are moving together with the same velocity $v_s = 10 \,ms^{-1}$ towards the hill.The sound reflects from the hill and returns to the observer.The frequency of the sound reflected from the hill, as heard by the observer, is given by the Doppler effect formula:$n' = n \left( \frac{v + v_s}{v - v_s} ight)$Where $v = 330 \,ms^{-1}$ is the speed of sound, $v_s = 10 \,ms^{-1}$ is the speed of the vehicle, and $n = 256 \,Hz$ is the original frequency.$n' = 256 \left( \frac{330 + 10}{330 - 10} ight) = 256 \left( \frac{340}{320} ight) = 256 	imes 1.0625 = 272 \,Hz$.The number of beats per second is the difference between the reflected frequency and the original frequency:$	ext{Beats} = n' - n = 272 \,Hz - 256 \,Hz = 16 \,Hz$.

$A$ vehicle sounding a whistle of frequency $256 \,Hz$ is moving on a straight road towards a hill with a velocity of $10 \,ms^{-1}$. The number of beats per second observed by a person travelling in the vehicle is (velocity of sound $= 330 \,ms^{-1}$).

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