Question

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 :

• A. Standing wave of frequency $\frac{1}{\sqrt{b}}$
• B. Wave moving in $+x$ direction with speed $\sqrt{\frac{a}{b}}$
• C. Wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$
• D. Standing wave of frequency $\sqrt{b}$

Answer 1

Answer: (C)

$y(x, t)=e^{-(\sqrt{a} x+\sqrt{b} t)^{2}}$
This is a wave travelling in $-x$ direction with speed
$\frac{\sqrt{b}}{\sqrt{a}}$