JEE Advanced 2023 — Paper 2 — Question 40

$S_{1}$ and $S_{2}$ are two identical sound sources of frequency 656 Hz . The source $S_{1}$ is located at $O$ and $S_{2}$ moves anticlockwise with a uniform speed $4 \sqrt{2} \mathrm{~m} \mathrm{~s}^{-1}$ on a circular path around O , as shown in the figure. There are three points $\mathrm{P}, \mathrm{Q}$ 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 $\mathrm{S}_{1}$ can move along direction OP. [Given: The speed of sound in air is $324 \mathrm{~m} \mathrm{~s}^{-1}$ ]

Consider both sources emitting sound. When $\mathrm{S}_{2}$ is at R and $\mathrm{S}_{1}$ approaches the detector with a speed $4 \mathrm{~m} \mathrm{~s}^{-1}$, the beat frequency measured by the detector is $\_\_\_\_$ Hz.