Question

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

• A. wave moving in - x direction, 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 + x direction, speed $\sqrt{\frac{a}{b}}$

Answer 1

Answer: (A)

$y\:\left(x,\:t\right)\:=\:e^{-\left(ax^2+\:bt^2\:+2\sqrt{ab\:xt}\right)}\:=\:e^{-\left(\sqrt{ax}+\sqrt{bt}\right)^2}$
It is a function of type y = $f \left(\omega t +kx\right) $
$ \therefore y \left(x,t\right)$ represents wave travelling along -x direction.
Speed of wave $= \frac{\omega}{k} = \frac{\sqrt{b}}{\sqrt{a}} =\sqrt{\frac{b}{a}}.$