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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+2ab cosx)` |
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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=(2pi)/(lambda)[(vt-x)+x_0]` and `phi_1=(2pi)/(lambda)(vt-x)` But `x_0=(lambda)/(2)` `therefore phi_2-phi_1=pi` Hence, phase difference, `phi =pi `: So, amplitude of the resultant wave `R=sqrt(a^2+b^2+2abcosphiz)` `=sqrt(a^2+b^2+2abcospi)` `=sqrt((a-b)^2)` `=a-b` or `R=|a-b|` |
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