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

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Question

(A) The Doppler effect formula for a moving source and a stationary detector is $f' = f \left( \frac{c}{c - v_s} \right)$,where $v_s$ is the component

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

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(A) The Doppler effect formula for a moving source and a stationary detector is $f' = f \left( \frac{c}{c - v_s} \right)$,where $v_s$ is the component of the source velocity along the line joining the source and the detector.In this circular motion,the velocity $v$ of the source is always tangential to the circle.The maximum frequency $f_{max}$ is detected when the source velocity component is directed towards the detector. This occurs when the velocity vector is along the line of sight. The component of velocity towards the detector is $v$. Thus,$f_{max} = f \left( \frac{c}{c - v} \right)$.The minimum frequency $f_{min}$ is detected when the source velocity component is directed away from the detector. This occurs when the velocity vector is along the line of sight. The component of velocity away from the detector is $v$. Thus,$f_{min} = f \left( \frac{c}{c + v} \right)$.The ratio of the largest to the smallest 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 the largest and smallest frequency detected by a detector $D$ at rest at a distance $2R$ from the center of the circle as shown in the figure? (Take $c$ as the speed of sound.)

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