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(B) For the interference of two waves,the resultant intensity is given by $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$.If the phase difference $\phi$ v

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$I = 10\,I_0$

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(B) For the interference of two waves,the resultant intensity is given by $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$.If the phase difference $\phi$ varies randomly with time,the average value of the cosine term is $(\cos \phi)_{av} = 0$.Therefore,the average resultant intensity becomes $I = I_1 + I_2$.For $n$ identical sources,each with intensity $I_0$,the total average intensity is the sum of the individual intensities: $I = I_0 + I_0 + \dots + I_0$ ($n$ times).Thus,$I = n\,I_0$.Given $n = 10$,the resultant intensity is $I = 10\,I_0$.

Consider ten identical sources of sound,all emitting the same frequency but having random phase angles. If the average intensity of each source is $I_0$,what will be the average resultant intensity $I$ due to all these ten sources?

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