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

The amplitudes of the waves area1=10μm,a2=4μm and a3=7μmand the phase difference between 1st and 2nd wave isπ2 and that between 2nd and 3rd wave is π2.Therefore, phase difference between 1st and 3rd is π. Combining 1st with 3rd, their resultant amplitude is given byA12=a12+a32+2a1a3cosϕ or  A1=102+72+2×10×7cosπ=100+49−140=9=3μm in the direction of first.Now combining this with 2nd wave we have, the resultant amplitudeA2=A12+a22+2A1a2cosπ2 or A=32+42+2×3×4cos90∘=9+16=5 μm