When only is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is __________. [2023]

Question

$S_{1}$ 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 $4 \sqrt{2} {ms}^{- 1}$ 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 direction OP.

[Given: The speed of sound in air is $324 {ms}^{- 1}$ ]

Q. When only $S_{2}$ is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is __________. [2023]

[Given: The speed of sound in air is $324 {ms}^{- 1}$ ]

Q. When only $S_{2}$ is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is __________. [2023]

Smart Achievers · Accepted Answer

(648)

$S_{2}$

$S_{1}$

$Velocity of source S_{2}, V_{s} = 4 \sqrt{2} \cos 45 °$

$From Doppler's effect, apparent frequency measured by the detector,$ $f = (\frac{V}{V + V_{s}}) f_{0}$

$= \frac{324}{324 + 4 \sqrt{2} \times \frac{1}{\sqrt{2}}} \times 656$

$= 648 Hz$

Solution

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Solution

Ans. (648) Given: velocity of sound V=324 m/s Frequency of source f0=656 Hz Velocity of source S2, Vs=42cos45° From Doppler's effect, apparent frequency measured by the detector, f=(VV+Vs)f0 =324324+42×12×656 =648 Hz

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