Question

The transverse displacement of a wave on string is given by $y( x , t )= e ^{-\left( ax ^{2}+ bt ^{2}+2 \sqrt{ ab } xt \right)}$ , this represents 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
$y=f( ax \pm bt )=f(x \pm vt )$
$y= e ^{-\left( ax ^{2}+ bt ^{2}+2 \sqrt{a b} xt \right)}= e ^{-(\sqrt{a x}+\sqrt{b t})^{2}}$
So, the wave will be travelling along - x-axis with speed $\sqrt{\frac{\textit{b}}{\textit{a}}}$ .