Question

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

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

Answer 1

Answer: (B)

General equation of travelling wave is
$y=\textit{f}\left(\textit{ax} \, \pm \textit{bt}\right)=\textit{f}\left(\textit{x} \, \pm \textit{vt}\right)$
$y= e ^{-\left(a x^{2}+b t^{2}+2 \sqrt{a b} x t\right)}= e ^{-(\sqrt{a} x+\sqrt{b} t)^{2}}$
So, the wave will be travelling along - x-axis with speed $\sqrt{\frac{\textit{b}}{\textit{a}}}$ .