InterviewSolution
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InterviewSolution
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Two waves are passing through a region in the same direction at the same time . If the equation of these waves are `y_(1) = a sin ( 2pi)/(lambda)( v t - x)` and `y_(2) = b sin ( 2pi)/( lambda) [( vt - x) + x_(0) ]` then the amplitude of the resulting wave for `x_(0) = (lambda//2)` isA. `| a - b|`B. ` a + b`C. `sqrt(a^(2) + b^(2))`D. `sqrt( a^(2) + b^(2) + 2 ab cos x)` |
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Answer» Correct Answer - A Let `phi_(1) and phi_(2)` represent angles of the first and second waves , then `phi_(2) = ( 2 phi)/( lambda ) [( vt - x) + x_(0)]` and `phi_(1) = ( 2pi)/(lambda) ( v t - x)` But `x_(0) = (lambda)/(2)`, ` phi_(2) - phi_(1) = pi` Hence , phase difference , `phi = pi `. So , amplitude of resultant wave `R sqrt(a^(2) + b^(2) + 2 ab cos phi)` ` = sqrt(a^(2) + b^(2) + 2 ab cos pi) = sqrt(( a - b)^(2)) = a - b` or `R = | a - b |` |
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