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(C) The apparent frequency is maximum when the component of the velocity of the source along the line joining the source and the observer is maximum t

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) The apparent frequency is maximum when the component of the velocity of the source along the line joining the source and the observer is maximum towards the observer.Let $O$ be the position of the observer and $C$ be the center of the circular path. The distance from the observer to the center is $OC = 9 + 8 = 17 \, m$.Let $P$ be the position of the tuning fork on the circle. The velocity vector $V_s$ of the tuning fork is tangential to the circle at $P$. The component of $V_s$ along $OP$ is maximum when the angle between $OP$ and the velocity vector $V_s$ is zero,or more simply,when the line $OP$ is tangent to the circle at $P$.In this configuration,$	riangle OPC$ is a right-angled triangle with the right angle at $P$ (since the radius $CP$ is perpendicular to the tangent $OP$).Using the Pythagorean theorem in $	riangle OPC$:$OP^2 + CP^2 = OC^2$$OP^2 + 8^2 = 17^2$$OP^2 = 289 - 64 = 225$$OP = \sqrt{225} = 15 \, m$.

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