A whistle revolves in a circle with angular speed $\omega=20 \mathrm{rad} \mathrm{s}^{-1}$ using a string of length $50 \mathrm{~cm}$. If the frequency of sound from the whistle is $385 \mathrm{~Hz}$, then what is the minimum frequency heard by an observer which is away from the centre $\left(v_{\text {sound }}=340 \mathrm{~ms}^{-1}\right)$ ?

• A

  $385 \mathrm{~Hz}$
• Correct answer
  B

  $375 \mathrm{~Hz}$
• C

  $394 \mathrm{~Hz}$
• D

  $333 \mathrm{~Hz}$

Solution

Velocity of source is given as $$ \begin{gathered} V_{\text {source }}=\text { rus }=0.5 \times 20 \\ =10 \mathrm{~ms}^{-1} \end{gathered} $$ $\therefore$ Minimum frequency is $f \mathrm{~min}$ $$ \begin{aligned} & =\left(\frac{V}{V+V_s}\right) f \\ & =\frac{340}{340+10} \times 385=374 \mathrm{~Hz} \end{aligned} $$

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