JEE Advanced 2023 · Paper 2 · Physics Q15

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PARAGRAPH I

$S_1$ 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 $4\sqrt2\ \mathrm{m\,s^{-1}}$ 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 $324\ \mathrm{m\,s^{-1}}$ ]

A circle centred at O, where source S1 sits. Points on the circle: R at the top, P at the bottom (diametrically opposite), Q at the right end of the horizontal diameter. Source S2 is on the circle between P and Q, moving anticlockwise (arrow near Q pointing up towards R). Dashed vertical and horizontal diameters through O.

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

Your answer

Answer and worked solution

Official answer: 8

$S_2$ at R. At the top of the circle its velocity is horizontal, perpendicular to the line RP. There is no Doppler shift: $f_2=656$ Hz.

$S_1$ approaches P at 4 m/s:
$f_1=656\times\frac{324}{324-4}=656\times\frac{324}{320}=664.2\ \text{Hz}.$

Beat frequency. $664.2-656=8.2$ Hz.

Topics:Beats Doppler effect

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JEE Advanced 2023 · Paper 2, Physics question 15