JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Waves & Sound

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise with a uniform speed $4\sqrt{2}{\mathrm{ms}}^{-1}$ on a circular path around $O$, as shown in the figure. There are three points $P,Q$ and $R$ on this path such that $P$ and $R$ are diametrically opposite while $Q$ is equidistant from them. A sound detector is placed at point $P$. The source $S_1$ can move along direction $OP$.
[Given: The speed of sound in air is $324{\mathrm{ms}}^{-1}$]

Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4{\mathrm{ms}}^{-1}$, the beat frequency measured by the detector is ____ Hz.