A whistle emitting a sound of frequency $440 ext{ Hz}$ is tied to a string of $1.5 ext{ m}$ length and rotated with an angular velocity of $20 ext{ rad s}^{-1}$ in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be ($v…

Question

A whistle emitting a sound of frequency $440	ext{ Hz}$ is tied to a string of $1.5	ext{ m}$ length and rotated with an angular velocity of $20	ext{ rad s}^{-1}$ in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be ($v = 330	ext{ ms}^{-1}$)

Aicharya · Accepted Answer

Velocity of source (or whistle), $v_s = R \omega = 30	ext{ ms}^{-1}$ Maximum frequency will be heard when whistle is at $P$ and minimum at $Q$. [The diagram shows a circular path of the whistle with point $P$ at the bottom, point $Q$ at the top, and observer $O$ on the horizontal line from the center] At $P : f_{\max} = f \left( \frac{v}{v - v_s} ight) = 440 \left( \frac{330}{330 - 30} ight) = 484	ext{ Hz}$ and At $Q : f_{\min} = f \left( \frac{v}{v + v_s} ight) = 440 \left( \frac{330}{330 + 30} ight) = 403.3	ext{ Hz}$

A whistle emitting a sound of frequency $440\text{ Hz}$ is tied to a string of $1.5\text{ m}$ length and…

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