A small source of sound vibrating at a freque | vedclass

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Question

(D) The linear velocity of the source,$v_s = r \omega$. Given $r = \frac{100}{\pi} ~cm = \frac{1}{\pi} ~m$ and angular frequency $\omega = 2 \pi f_{ro

Vedclass · Accepted Answer

$485.4 ~Hz, 515.5 ~Hz$

Vedclass · Answer

(D) The linear velocity of the source,$v_s = r \omega$. Given $r = \frac{100}{\pi} ~cm = \frac{1}{\pi} ~m$ and angular frequency $\omega = 2 \pi f_{rot} = 2 \pi 	imes 5 = 10 \pi ~rad/s$. Thus,$v_s = \frac{1}{\pi} ~m 	imes 10 \pi ~rad/s = 10 ~m/s$. Using the Doppler effect formula for a moving source and stationary observer: $f' = f \left( \frac{v}{v \mp v_s} ight)$. The maximum frequency occurs when the source moves towards the listener: $f_{max} = 500 	imes \left( \frac{332}{332 - 10} ight) = 500 	imes \frac{332}{322} \approx 515.5 ~Hz$. The minimum frequency occurs when the source moves away from the listener: $f_{min} = 500 	imes \left( \frac{332}{332 + 10} ight) = 500 	imes \frac{332}{342} \approx 485.4 ~Hz$.

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