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(A) The Doppler effect formula for frequency heard by an observer is $n' = n \left( \frac{v + v_o}{v - v_s} \right)$,where $v_o$ is the velocity of th

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Observer will hear maximum frequency at $P$ if source is at $B$

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(A) The Doppler effect formula for frequency heard by an observer is $n' = n \left( \frac{v + v_o}{v - v_s} ight)$,where $v_o$ is the velocity of the observer towards the source and $v_s$ is the velocity of the source towards the observer.For maximum frequency,the relative velocity of approach $(v_o + v_s)$ must be maximum.At $t=0$,source is at $A$ and observer is at $Q$. The angular position of the source is $	heta = \omega t$. The observer's position is $x = A \sin(\omega t + \phi)$. Given $T = 2\pi/\omega$,the observer and source are synchronized.At $P$,the observer's velocity is maximum towards the right. For maximum frequency,the source must have a maximum velocity component towards the observer (i.e.,towards the right).When the source is at $B$,its velocity is directed towards $A$ (horizontal). When the source is at $D$,its velocity is directed towards $C$ (horizontal). Specifically,at $B$,the velocity vector is horizontal to the right. At $P$,the observer is moving with maximum velocity towards the right. Thus,the relative velocity of approach is maximized when the source is at $B$ and the observer is at $P$.

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