Question 37: Waves

Question

$S_1$ and $S_2$ are two identical sound sources of frequency $656 \mathrm{~Hz}$. The source $S_1$ is located at $O$ and $S_2$ moves anti-clockwise 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 $P, Q$ 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 $O P$.
[Given: The speed of sound in air is $324 \mathrm{~m} \mathrm{~s}^{-1}$ ]

Accepted Answer

$\begin{gathered}f_0=656 \mathrm{~Hz} \\ 	ext { Velocity of second }=324 \mathrm{~m} \mathrm{~s}^{-1}\end{gathered}$
Velocity of the source away from detector,
$$
\begin{aligned}
v_{\mathrm{s}} & =4 \sqrt{2} \cos 45^{\circ}=4 \mathrm{~m} \mathrm{~s}^{-1} \\
	herefore \quad f & =\left(\frac{v}{v+v_s}ight) f_0 \\
& =\left(\frac{324}{324+4}ight) 	imes 656=648 \mathrm{~Hz}
\end{aligned}
$$

Waves

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