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
IIT 2015, Medium
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First and fourth wave interfere destructively. So from the interference of $2^{\text {nd }}$ and $3^{\text {rd }}$ wave only,
$\Rightarrow I _{2 e \varepsilon}= I _0+ I _0+2 \sqrt{ I _0} \sqrt{ I _0} \cos \left(\frac{2 \pi}{3}-\frac{\pi}{3}\right)=3 I _0$
$\Rightarrow n =3$
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