Three coherent waves having amplitude 12,6,4 mm arrive at a given point with successive phase difference pie/ 2 then the amplitude of resultant wave is?

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Solution

Let
x1 = 12 sin(wt)
x2 = 6 sin(wt + pie/2) = 6 cos(wt)
x3 = 4 sin(wt + pie) = -4 sin(wt)

x = x1 + x2 + x3
= 12sin(wt) + 6 cos(wt) - 4sin(wt)
= 8sin(wt) + 6cos(wt)

Let R be the resultant amplitude.
8 = Rcos(f)
6 = Rsin(f)

x = Rcos(f)sin(wt) + Rsin(f)cos(wt)
x = Rsin(wt + f)

R = root(8^2 + 6^2)
= root(100)
= 10

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