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Need for Intensity

Four harmonic...

Question

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

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Solution

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

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