Question

Two identical sources of sound of same frequency and identical intensities $I_0$ 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. $I_0$
• B. $2I_0$
• C. $4I_0$
• D. Zero

Answer 1

The correct option is B $2I_0$

Given : $I_1=I_2=I_o$

Resultant intensity $I=I_1+I_2+2\sqrt{I_1{I}_2}cos\delta$

where $\delta$ is the phase difference.

$I=I_o+I_o+2\sqrt{I_o\times I_o}cos\delta =2(1+cos\delta )$

$⟹I=4I_{o}co{s}^2\frac{\delta }{2}$

Now average intensity $<I>=4I_o<co{s}^2\frac{\delta }{2}>$

$<I>=4I_o\times \frac{1}{2}=2I_o$