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 (velocity of sound in air $330\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$ ) is
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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

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

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

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

${\mathrm{f}}^{}=100\left(1+\frac{3.7}{330}\right)=103\mathrm{H}\mathrm{z}$

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