The transverse displacement y(x, t) of a wave | vedclass

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(A) The given equation is $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$.This can be rewritten as $y(x, t) = e^{-(\sqrt{a}x + \sqrt{b}t)^2}$.$A$ wave f

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wave moving in $-x$ direction,speed $\sqrt{\frac{b}{a}}$

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(A) The given equation is $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$.This can be rewritten as $y(x, t) = e^{-(\sqrt{a}x + \sqrt{b}t)^2}$.$A$ wave function representing a travelling wave is generally of the form $f(kx + \omega t)$ or $f(kx - \omega t)$.Comparing this with the form $f(kx + \omega t)$,where $k = \sqrt{a}$ and $\omega = \sqrt{b}$,we see that the wave is moving in the $-x$ direction.The speed of the wave $v$ is given by $v = \frac{\omega}{k} = \frac{\sqrt{b}}{\sqrt{a}} = \sqrt{\frac{b}{a}}$.Therefore,the wave is moving in the $-x$ direction with a speed of $\sqrt{\frac{b}{a}}$.

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents a

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