A whistle S of frequency f revolves in a circ | vedclass

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Question

(A) Let $c$ be the speed of sound. The detector $D$ is at a distance $2R$ from the center of the circle. The source $S$ moves in a circle of radius $R

Vedclass · Accepted Answer

$\left(\frac{c+v}{c-v}\right)$

Vedclass · Answer

(A) Let $c$ be the speed of sound. The detector $D$ is at a distance $2R$ from the center of the circle. The source $S$ moves in a circle of radius $R$ with speed $v$. The component of the source's velocity along the line joining the source and the detector determines the Doppler shift.The maximum frequency is detected when the source is moving directly towards the detector. At this point,the velocity component along the line $SD$ is $v$. The observed frequency is $f_{max} = f \left( \frac{c}{c-v} \right)$.The minimum frequency is detected when the source is moving directly away from the detector. At this point,the velocity component along the line $SD$ is $v$. The observed frequency is $f_{min} = f \left( \frac{c}{c+v} \right)$.Therefore,the ratio of maximum to minimum frequency is:$\frac{f_{max}}{f_{min}} = \frac{f \left( \frac{c}{c-v} \right)}{f \left( \frac{c}{c+v} \right)} = \frac{c+v}{c-v}$.

$A$ whistle $S$ of frequency $f$ revolves in a circle of radius $R$ at a constant speed $v$. What is the ratio of maximum and minimum frequency detected by a detector $D$ at rest at a distance $2R$ from the center of the circle as shown in the figure?

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