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

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The transverse displacement y(x, t) of a wave on a string is given by

$y (x, t) = e^{- ({ax}^{2} + {bt}^{2} + 2 \sqrt{ab} xt)}$

wave moving in +x direction with speed

standing wave of frequency

wave moving in –x direction with speed

standing wave of frequency

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$y (x, t) = e^{- {[\sqrt{a} x + \sqrt{b} t]}^{2}}$

It is transverse type $y (x, t) = e^{- {(ax + bt)}^{2}}$

Speed $v = \frac{\sqrt{b}}{\sqrt{a}}$

and wave is moving along –x direction.

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