Doppler Effect

Question

A whistle revolves in a circle with angular speed ω = 20 rad/s using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer far away from the centre? (Velocity of sound v = 340 m/s)

RankGuru · Accepted Answer

1. **Source Velocity ($v_s$)**: $v_s = r\omega = (0.50	ext{ m})(20	ext{ rad/s}) = 10	ext{ m/s}$.
2. **Doppler Condition**: Minimum frequency is heard when the source is moving directly AWAY from the observer.
3. **Formula**: $f' = f \left(\frac{v}{v + v_s}ight)$.
4. **Calculation**: $f' = 385 \left(\frac{340}{340 + 10}ight) = 385 	imes \frac{340}{350} = 385 	imes \frac{34}{35} = 11 	imes 34 = 374	ext{ Hz}$.

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