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
34μW/m2, if the sources are incoherent.
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B
4μW/m2, if the sources are coherent but out of phase.
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C
25μW/m2, if S1 is switched off.
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D
64μW/m2, if the sources are coherent and in phase.
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Solution
The correct option is D64μW/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=25μW/m2 I2=0.9π4π(5)2=91000mW/m2=9μW/m2
For incoherent interference, I=I1+I2=34μW/m2
For coherent interference,
when ϕ=π, I=(√I1−√I2)2=4μW/m2
When ϕ=0 I=(√I1+√I2)2=64μW/m2