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Question:

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, π/3, 2π/3, and π. When they are superposed, the intensity of the resulting wave is nI0. The value of n is?

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 π/3 between them is
2Acos(π/6) = √3A
Intensity I ∝ A² ⇒ I = 3A² ⇒ n = 3