A source of sound $\mathrm{S}$ emitting waves of frequency $\text{100 Hz }$and an observer $\text{O}$ are located at some distance from each other. The source is moving with a speed of $19.4\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$ at an angle of ${60}^{\mathrm{o}}$ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer corresponding to the wave emitted by the source at the instant shown is (velocity of sound in air $330\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$ )
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• Correct answer
  A

  $\text{103}\text{Hz}$
• B

  $\text{106}\text{Hz}$
• C

  $\text{97}\text{Hz}$
• D

  $\text{100}\text{Hz}$

Solution

${\mathrm{f}}^{}={\mathrm{f}}_0\left(\frac{\mathrm{v}-{\mathrm{v}}_{\mathrm{0}}}{\mathrm{v}-{\mathrm{v}}_{\mathrm{s}}}\right)$

${\mathrm{f}}^{}=100\left(\frac{\mathrm{v}-0}{\mathrm{v}-\left(+9.7\right)}\right)$

${\mathrm{f}}^{}=100\frac{\mathrm{v}}{\mathrm{v}\left(1-\frac{9.7}{\mathrm{v}}\right)}$

${\mathrm{f}}^{}=100\left(1+\frac{9.7}{330}\right)=\mathrm{103 }\mathrm{H}\mathrm{z}$

Hence, the correct answer is option: 'A'.