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  4. Two sinusoidal waves of intensity I having same frequency and same amplitude interferes constructively at a point. The resultant intensity at a point will be

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Q. Two sinusoidal waves of intensity $I$ having same frequency and same amplitude interferes constructively at a point. The resultant intensity at a point will be

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Solution:

The resultant intensity is given by
$I_{R}=I_{1}+I_{2}+2\sqrt{I_{1}I_{2}} cos\phi=1$
For constructive interference, cos$\phi = 1$
$\therefore \, I_{R}=I_{1}+I_{2}+2\sqrt{I_{1}I_{2}}$
or $\, I_{R}=4I\quad\left(Given I_{1}=I_{2}=I\right)$