The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t) = e^{-\left(ax^{2}+bt^{2}+2\sqrt{ab}xt\right)}$. This represents a\\
(1) wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$\\
(2) standing wave of frequency $\sqrt{b}$\\
(3) standing wave of frequency $\frac{1}{\sqrt{b}}$\\
(4) wave moving in $+x$ direction with speed $\sqrt{\frac{a}{b}}$