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. (a) `4`B. (b) `5`C. (c) `6`D. (d) `7` |
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Answer» Correct Answer - B The amplitudes of the waves are `a_1=10mum`, `a_2=4mum` and `a_3=7mum` and the phase difference between 1st and 2nd wave is `pi/2` and that between 2nd and 3rd wave is `pi/2`. Therefore, phase difference between 1st and 3rd is `pi`. Combining 1st with 3rd, their resultant amplitude is given by `A_1^2=a_1^2+a_3^2+2a_1a_3cos varphi` or `A_1=sqrt(10^2+7^2+2xx10xx7cos pi)` `=sqrt(100+49-140)` `=sqrt9=3mum` in the direction of first. Now combining this with 2nd wave we have, the resultant amplitude `A^2=A_1^2+a_2^2+2A_1a_2cospi/2` or `A=sqrt(3^2+4^2+2xx3xx4cos 90^@)=sqrt(9+16)` `=5mum` |
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