InterviewSolution
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InterviewSolution
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Three waves of equal frequency having amplitudes `10mum`, `4mum`, `7mum` arrive at a given point with successive phase difference of `pi//2`, the amplitude of the resulting wave in `mum` is given byA. 4B. 5C. 6D. 7 |
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Answer» Correct Answer - B The amplitude of the waves are `a_(1)=10mum,a_(2)=4mu m and a_(3)=7mu m` and phase difference between Ist and IInd wave is `(pi)/(2)` and that between Iind and IIIrd wave is `(pi)/(2)`. Then, phase difference between Ist and IIIrd is `pi`. Combining Ist with IIIrd, their resultant amplitude is given by `A_(1)^(2)=a_(1)^(2)+a_(3)^(2)=2a_(1)a_(3) cos phi` `or A_(1)=sqrt(10^(2)+7^(2)+2xx10xx7 cos pi)` `=sqrt(100+49-140)=sqrt(9)=3 mu m` Now, combining this with IInd wave, we have the resultant amplitude `A^(2)=A_(1)^(2)+a_(2)^(2)+2A_(1)a_(2) "cos"(pi)/(2)` `or A=sqrt(3^(2)+4^(2)+2xx3xx4xxcos90^(@))` `=sqrt(9+16)=sqrt(25)=5mu m` |
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