A whistle of frequency 660 ,Hz moves in a cir | vedclass

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Question

(D) Given:Frequency of the whistle, $f_0 = 660 \,Hz$Speed of sound, $v = 340 \,m/s$Angular speed of the whistle, $\omega = 10 \,rad/s$Radius of the ci

Vedclass · Accepted Answer

$680$

Vedclass · Answer

(D) Given:Frequency of the whistle, $f_0 = 660 \,Hz$Speed of sound, $v = 340 \,m/s$Angular speed of the whistle, $\omega = 10 \,rad/s$Radius of the circle, $r = 1 \,m$The linear velocity of the whistle is given by $v_s = \omega r = 10 	imes 1 = 10 \,m/s$.Since the listener is at a long distance from the center of the circle, the velocity component of the whistle along the line joining the whistle and the listener is maximum when the whistle moves directly towards the listener.Using the Doppler effect formula for a source moving towards a stationary observer:$f = f_0 \left( \frac{v}{v - v_s} ight)$Substituting the values:$f = 660 	imes \left( \frac{340}{340 - 10} ight)$$f = 660 	imes \left( \frac{340}{330} ight)$$f = 2 	imes 340 = 680 \,Hz$Thus, the highest frequency heard by the listener is $680 \,Hz$.Therefore, the correct option is $D$.

$A$ whistle of frequency $660 \,Hz$ moves in a circle of radius $1 \,m$ at an angular speed of $10 \,rad/s$. The highest frequency heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound $= 340 \,m/s$.) (in $\,Hz$)

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