Q. 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
A) $I = 100I_{0}$
B) $I = 10I_{0}$
C) $I = I_{0}$
D) $I = \sqrt{10}I_{0}$
Explanation
(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 $\left( \cos\phi \right)_{av} = 0$
$\Rightarrow I = I_{1} + I_{2}$
For $n$ identical waves, $I = I_{0} + I_{0} + \ \ldots.\ = nI_{0}$
Here $I = 10I_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.