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A whistle revolves in a circle with angular speed ω = 20 rad/sec 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 which is far away from the centre : - (Vsound = 340 m/s)
A
385 Hz
B
374 Hz
C
394 Hz
D
333 Hz
Detailed Solution
Speed of the whistle: $v_s = \omega R = 20 \times 0.5 = 10$ m/s.
The minimum frequency is heard when the whistle is moving directly away from the observer:
$n_{min} = n_0\left(\dfrac{V}{V + \omega R}\right) = 385 \times \dfrac{340}{340 + 10} = 385 \times \dfrac{340}{350}$
$n_{min} = 374$ Hz
(The maximum, when it moves towards the observer, is $n_0\dfrac{V}{V - \omega R} = 385 \times \dfrac{340}{330} \approx 397$ Hz.)
The minimum frequency is heard when the whistle is moving directly away from the observer:
$n_{min} = n_0\left(\dfrac{V}{V + \omega R}\right) = 385 \times \dfrac{340}{340 + 10} = 385 \times \dfrac{340}{350}$
$n_{min} = 374$ Hz
(The maximum, when it moves towards the observer, is $n_0\dfrac{V}{V - \omega R} = 385 \times \dfrac{340}{330} \approx 397$ Hz.)