Question

Four harmonic waves of equal frequencies and equal intensities I${}_0$ have phase angles 0, $\pi$/3, 2$\pi$/3, and $\pi$. When they are superposed, the intensity of the resulting wave is nI${}_0$. The value of n is

Answer 1

Let the amplitude of each wave is A.
The ones having phases of 0 and $\pi$ will cancel each other.
Resultant of other two is having angle $\frac{\pi }{3}$ between them is $2A\cos \frac{\pi }{6}=\sqrt{3}A$
Intensity $I\propto A^2$
$\Rightarrow I=3A^2$
$\Rightarrow n=3$