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(D) The source of sound is moving in a circular path. When the source moves towards the observer,the observed frequency is maximum,and when it moves a

Vedclass · Accepted Answer

$485.4 Hz, 515.5 Hz$

Vedclass · Answer

(D) The source of sound is moving in a circular path. When the source moves towards the observer,the observed frequency is maximum,and when it moves away,the observed frequency is minimum. The observer is at rest.Given:Frequency of source $f_0 = 500 Hz$Radius $r = \frac{100}{\pi} cm = \frac{1}{\pi} m$Angular speed $n = 5 rev/s$Angular velocity $\omega = 2\pi n = 2\pi 	imes 5 = 10\pi rad/s$Speed of source $v_s = \omega r = (10\pi) 	imes (\frac{1}{\pi}) = 10 m/s$Speed of sound $v = 332 m/s$Using the Doppler effect formula for a moving source and stationary observer:$f = f_0 \left( \frac{v}{v \mp v_s} ight)$Maximum frequency (source moving towards observer):$f_{max} = 500 \left( \frac{332}{332 - 10} ight) = 500 \left( \frac{332}{322} ight) \approx 515.5 Hz$Minimum frequency (source moving away from observer):$f_{min} = 500 \left( \frac{332}{332 + 10} ight) = 500 \left( \frac{332}{342} ight) \approx 485.4 Hz$Thus,the minimum and maximum frequencies are $485.4 Hz$ and $515.5 Hz$ respectively.

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