Consider ten identical sources of sound all giving the same frequency but having phase angles which are random. If the average intensity of each source is ${I_0}$, the average of resultant intensity $I$ due to all these ten sources will be
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(b) In case of interference of two waves resultant intensity
$I = {I_1} + {I_2} + 2\sqrt {{I_1}{I_2}} \cos \phi $
If $\phi$ varies randomly with time, so
$I = {I_1} + {I_2} + 2\sqrt {{I_1}{I_2}} \cos \phi $
If $\phi$ varies randomly with time, so
${(\cos \phi )_{av}} = 0$ ==> $I = {I_1} + {I_2}$
For $n$ identical waves, $I = {I_0} + {I_0} + ....... = n\,{I_0}$
here $I = 10{I_0}.$
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