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Question

A whistle emitting a loud sound of frequency 540Hz is whirled in a horizontal circle of radius 2m and at a constant angular speed of 15rad/s. The speed of sound is 330m/s. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the center of the circle is?

A
1.0
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B
1.1
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C
1.2
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D
1.4
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Solution

The correct option is C 1.2
Original frequency of the source fo=540 Hz
Velocity of sound in air vsound=330m/s
Angular velocity of the source w=15rad/s
Radius of circular orbit r=2m
Thus linear velocity of the source vsource=rw
vsource=2×15=30 m/s
Using Doppler effect when a source moves towards the stationary observer.
Highest frequency heard by the observer f1=fo[vsoundvsoundvsource]
f1=540[33033030]=540[330300]
Using Doppler effect when a source moves away from the stationary observer.
Lowest frequency heard by the observer f2=fo[vsoundvsound+vsource]
f2=540[330330+30]=540[330360]
Thus ratio of frequencies f1f2=(540×330)/300(549×330)/360
f1f2=360300=1.2

678302_632579_ans_ee1b48455fd44e0d898cb8f9379648e1.png

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