JEE Advanced 2023 Paper 2 · Q15 · Sound Waves

Question

PARAGRAPH I (continued) — Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4$ m·s$^{-1}$, the beat frequency measured by the detector is ___ Hz.

SolveKar AI · Accepted Answer

$S_2$ at $R$ (diametrically opposite to $P$): velocity tangential, direction perpendicular to $S_2P$ at the moment, so radial velocity of $S_2$ relative to detector is zero — $S_2$ contributes $f_2 = 656$ Hz. $S_1$ approaches $P$ at $4$ m/s: $f_1' = f\cdot v/(v - v_s) = 656\cdot 324/320 = 664.2$ Hz. Beat frequency $= |f_1' - f_2| = 664.2 - 656 = 8.2$ Hz.

JEE Advanced 2023 Paper 2 · Q15 · Sound Waves

Solution