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Question

Two identical speakers, emit sound waves of frequency 103 Hz uniformly in all directions.
The audio output of each speaker is 9π10 mW. A point P is at a distance of 3 m from S1 and 5 m from S2. Resultant intensity of sound at P is

A
34 μW/m2, if the sources are incoherent.
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B
4 μW/m2, if the sources are coherent but out of phase.
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C
25 μW/m2, if S1 is switched off.
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D
64 μW/m2, if the sources are coherent and in phase.
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Solution

The correct option is D 64 μW/m2, if the sources are coherent and in phase.
Intensity at a distance r from a sound of power output P is given by I=P4πr2
I1=0.9π4π(3)2=140mW/m2=25 μW/m2
I2=0.9π4π(5)2=91000mW/m2=9 μW/m2
For incoherent interference,
I=I1+I2=34 μW/m2

For coherent interference,
when ϕ=π,
I=(I1I2)2=4 μW/m2
When ϕ=0
I=(I1+I2)2=64 μW/m2

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