InterviewSolution
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InterviewSolution
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The transverse displacement `y(x, t)` of a wave on a string is given by `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)`. This represents a :A. (a) wave moving in -x direction with speed `sqrt((b)/(a))`B. (b) standing wave of frequency `sqrt(b)`C. ( c ) standing wave of frequency `(1)/sqrt(b)`D. (d) wave moving in +x direction with speed `sqrt((a)/(b))` |
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Answer» Correct Answer - A (a) Given wave equation is `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)` `= e^(-[sqrt(ax^(2)) + (sqrt(bt))^(2) + 2sqrt(a x). sqrt(b t)] = e^(-(sqrt(ax) + sqrt(bt)^(2))` `=e^(-(x+ sqrt(b/a) t)^2` It is a function of type `y = f(x + vt)` rArr Speed of wave `= sqrt((b)/(a))` |
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