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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. wave moving in - x-direction with speed `sqrt((b)/(a))`B. standing wave of frequency `sqrt(b)`C. standing wave of frequency `(1)/(sqrt(b))`D. wave moving in + x-direction with speed `sqrt(a//b)` |
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Answer» Correct Answer - A `y(x, t) = e^(-(ax^(2)+bt^(2)+2sqrt(ab) xt))=e^(-(sqrt(a)x+sqrt(b)t)^(2)` It is a function of type `y = f(omega t + kx)` `therefore y (x, t)` represents wave travelling along - x-direction, Speed of wave = `(omega)/(k)=(sqrt(b))/(sqrt(a))=sqrt((b)/(a))` |
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