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Derive the expression for the resultant displacement and amplitude when two waves having the same amplitudeand a phase differenceof phi superpose. |
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Answer» Solution :Consider TWO WAVES having the same AMPLITUDE a and a phasedifference of `phi`. Let the displacement produced by source `S_1` be by `y_1` = a cos wt and by `S_2` be the `y_2=a cos (wt + phi)` The RESULTANT displacement `y=y_1+y_2` `y=a cos wt + a cos (wt + phi)` Using the formula , cos A + cos B = 2cos `((A+B)/2)cos ((A-B)/2)` `y=a[cos wt + cos (wt + phi)]=2A cos ((wt+wt+phi)/2)cos ((wt-wt+phi)/2)` `y=2a cos ((2wt+phi)/2) cos (phi/2)=2acos phi/2 cos ((2wt+phi)/2)` The amplitude of the resultantdisplacement is = `2a cos phi/2` |
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