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Question

Two identical sources of sound of same frequency and identical intensities I0 are producing sound. If their phases are irregular, then the average intensity of sound at a point where waves from the two sources are superposing is

A
I0
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B
2I0
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C
4I0
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D
Zero
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Solution

The correct option is B 2I0
Given : I1=I2=Io

Resultant intensity I=I1+I2+2I1I2cosδ
where δ is the phase difference.

I=Io+Io+2Io×Iocosδ=2(1+cosδ)

I=4Iocos2δ2

Now average intensity <I>=4Io<cos2δ2>

<I>=4Io×12=2Io

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