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  4. A source of sound S emitting waves of frequency 100 Hz and an observor O are located at some distance from each other. The source is moving with a speed of 19.4 m s-1 at an angle of 60° with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air 330 ms -1 )

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Q. A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4\, m s^{-1}$ at an angle of $60^{\circ}$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330\, ms ^{-1}$ )Physics Question Image

BITSATBITSAT 2016

Solution:

Here, original frequency of sound, $f_{0}=100 \,Hz$
Speed of source $V_{s} 19.4 \cos 60^{\circ}=9.7$
From Doppler's formula
$f^{1}=f_{0}\left(\frac{V-V_0}{V-V_{s}}\right)$
$f^{1}=100\left(\frac{V-0}{V-(+9.7)}\right)$
$f^{1} 100 \frac{V}{V\left(1-\frac{9.7}{V}\right)}$ $f^{1}=100\left(1+\frac{9.7}{330}\right)=103 \,Hz$
Apparent frequency $f^{1}=103 \,Hz$

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