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

• A
  wave moving in negative $x$-direction with speed $\sqrt{\frac{b}{a}}$
• B
  standing wave of frequency $\sqrt{b}$
• C
  standing wave of frequency $\frac{1}{\sqrt{b}}$
• D
  wave moving in positive $x$-direction with speed $\sqrt{\frac{b}{a}}$