A source of sound S emitting waves of frequency 100 Hz and an...

A source of sound S emitting waves of frequency

100 \mathrm{ Hz}

and an observor

\mathrm{O}

are located at some distance from each other. The source is moving with a speed of

19.4 \mathrm{ ms}^{-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 \mathrm{ ms}^{-1}

)

A source of sound S emitting waves of frequency 100 Hz and an observor O are located at some distance from each other.

Options

A $103 \mathrm{ Hz}$
B $106 \mathrm{ Hz}$
C $97 \mathrm{ Hz}$
D $100 \mathrm{ Hz}$

Correct answer

A. $103 \mathrm{ Hz}$

Step-by-step solution

Here, original frequency of sound,

\mathrm{f}_{0}=100 \mathrm{ Hz}

Speed of source

V_{s}=19.4 \cos 60^{{}^{\circ}}=9.7

From Doppler's formula

\mathrmf^{\mathrm{l}}=\mathrm{f}_{0}\left(\frac{\mathrm{V}-\mathrm{V}_{0}}{\mathrm{ V}-\mathrm{V}_{\mathrm{s}}}\right)\mathrmf^{\mathrm{l}}=100\left(\frac{\mathrm{V}-0}{\mathrm{ V}-(+9.7)}\right)\mathrmf^{\mathrm{l}}=100 \frac{\mathrm{V}}{\mathrm{V}\left(1-\frac{9.7}{\mathrm{ V}}\right)}\mathrmf^{1}=100\left(1+\frac{9.7}{330}\right)=103 \mathrm{ Hz}

Apparent frequency

\mathrmf^{1}=103 \mathrm{ Hz}

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