## Question

Three waves of equal frequency having amplitude 10 μm, 4 μm and 7μ arrive at a given point with a successive phase difference of π/2. The amplitude of the resulting wave in μ m is given by

### Solution

5

The amplitude of the three waves are *a*_{1} = 10 μm, *a*_{2} = 4 μm and *a*_{3} = 7 μm. Let the phase of the first wave be zero. Then the wave of the second wave = π/2 and of third wave Therefore, the phase difference between the first wave and third wave is π. Hence their resultant is

The phase difference between this resultant (of first and third waves) and the second wave = π/2. Therefore, the resultant of *a* and *a*_{3} is

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