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Question:

Two sinusoidal waves of intensity I having the same frequency and same amplitude interfere constructively at a point. The resultant intensity at that point will be:

4I

2I

8I

I

Solution:

For two interfering waves, the resultant intensity is given by:
IR = I1 + I2 + 2√(I1I2)cosφ
Since frequencies are the same, intensity is directly proportional to the square of the amplitude. For constructive interference, φ = 0, and with I1 = I2 = I, we get
IR = 4I