Question

# Two identical sources of sound of same frequency and identical intensities $$\displaystyle I_0$$ 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
I0
B
2I0
C
4I0
D
Zero

Solution

## The correct option is B $$\displaystyle 2 I_0$$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. $$I = I_o + I_o + 2 \sqrt{I_o \times I_o} cos \delta = 2 (1 + cos \delta)$$  $$\implies I = 4 I_o cos^2 \dfrac{\delta}{2}$$Now average intensity       $$< I > = 4I_o <cos^2 \dfrac{\delta}{2}>$$ $$< I > = 4I_o \times \dfrac{1}{2} = 2 I_o$$Physics

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