A whistle of frequency $660 \mathrm{~Hz}$ moves in a circle of radius $1 \mathrm{~m}$ at an angular speed of $10 \mathrm{rad} / \mathrm{s}$. The highest frequency heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound $=340 \mathrm{~m} / \mathrm{s}$.)

• A

  $700 \mathrm{~Hz}$
• B

  $640 \mathrm{~Hz}$
• C

  $720 \mathrm{~Hz}$
• Correct answer
  D

  $680 \mathrm{~Hz}$

Solution

Given, frequency whistle $f_0=660 \mathrm{~Hz}$, speed of sound $=340 \mathrm{~m} / \mathrm{s}$ angular speed of whistle, $\omega=10 \mathrm{rad} / \mathrm{s}$ and radius of circle, $r=1 \mathrm{~m}$. Since, we know that the maximum frequency heard by listener, if whistle has tangential velocity towards the listener as shown in figure,
linear velocity, $v=\omega r$ $=10 \times 1=10 \mathrm{~m} / \mathrm{s}$ As, given that, there is long distance between whistle and listener i.e., $\theta \approx 0$. Now, the apparent frequency, $\begin{aligned} & f=\frac{f_0 v}{v-v_s} \\ & f=\frac{660 \times 340}{340-10}=680 \mathrm{~Hz}\end{aligned}$ Hence, the correct option is (d).

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