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 $\sqrt{\text{b}}$
• D. Standing wave of frequency $\frac{1}{\sqrt{\text{b}}}$

Answer 1

Answer: (B)

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