Q.
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 are a1=10μm,a2=4μm and a3=7μm
and the phase difference between 1st and 2 nd wave is 2π and that between 2 nd and 3 rd wave is 2π.
Therefore, phase difference between 1st and 3rd is π. Combining 1st with 3rd, their resultant amplitude is given by A12=a12+a32+2a1a3cosϕ
or A1=102+72+2×10×7cosπ =100+49−140 =9=3μm in the direction of first.
Now combining this with 2 nd wave we have, the resultant amplitude A2=A12+a22+2A1a2cos2π
or A=32+42+2×3×4cos90∘ =9+16 =5μm