The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}$ This represents a
Medium
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(a)
$y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}=e^{-(\sqrt{a} x+\sqrt{b} t)^2}$
It is a function of type
$y=f(\omega t+k x)$
$\therefore y(x, t)$ represents wave travelling along
$-x$ direction.
Speed of wave $=\frac{\omega}{k}=\frac{\sqrt{b}}{\sqrt{a}}=\sqrt{\frac{b}{a}}$.
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