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

wave moving in –x direction with speed $\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$

standing wave of frequency $\sqrt{b}$

standing wave of frequency $\frac{1}{\sqrt{b}}$

wave moving in +x direction with speed $\sqrt{\frac{a}{b}}$