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Question

A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius 100/π cm at a constant angular speed of 5.0 revolutions per second. A listener situation situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. Speed of sound in air = 332 m s−1.


Solution

Given:
Speed of sound in air v = 332 ms−1
Radius of the circle r100π cm = 1π m
Frequency of sound of the source f0 = 500 Hz
Angular speed ω = 5 rev/s
Linear speed of the source is given by:
 v=ωr
⇒ v=5×1π=5π=1.59 m/s

 ∴ velocity of source vs = 1.59 m/s

Let X be the position where the observer will listen at a maximum and Y be the position where he will listen at the minimum frequency.



Apparent frequency f1 at X is given by:

f1=vv-vsf0

On substituting the values in the above equation, we get:
f1=332332-1.59×500515 Hz

Apparent frequency f2 at Y is given by:

f2=vv+vsf0

On substituting the values in the above equation, we get:
f2=332332+1.59×500485 Hz

Physics
HC Verma - I
Standard XI

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