Question 522: Waves

Question

A whistle revolves in a circle with angular speed $$\omega $$ = 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 which is far away from the centre  (velocity of sound $$=$$ 340 m/s)

Accepted Answer

The whistle is revolving in a circle of radius 50 cm. So the source (whistle) is moving and the observer is fixed.
The minimum frequency will be heard by the observer when the linear velocity of the whistle (source) will be in a direction as shown in the figure, i.e. when the source is receding.
The apparent frequency heard by the observer is then
given by $$\upsilon ' = \upsilon \left( {{v \over {V + v}}} ight)$$
where V and v are the velocities of sound and source respectively and $$\upsilon $$ is the actual frequency.
Now $$v = r\omega  = 0.5 	imes 20 = 10\,m/s$$
V = 340 m/s,  $$\upsilon $$ = 385 Hz.
$$ 	herefore $$ $$\upsilon ' = 385 	imes {{340} \over {340 + 10}} = 374$$ Hz

Answer

385 Hz

Answer

374 Hz

Answer

394 Hz

Answer

333 Hz.

Waves

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

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