Q. The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t) = e^{- \left( ax^{2} + bt^{2} + 2\sqrt{ab}xt \right)}$ This represent a
A) Wave moving in x- direction with 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 with speed $\sqrt{\frac{a}{b}}$
Explanation
(a) $y(x,t) = e^{- \left( ax^{2} + bt^{2} + 2\sqrt{ab}tx \right)}$
$= e^{- \left( \sqrt{a}x + \sqrt{b}t \right)^{2}}$
It is a function of type
∴ y(x,t) represents wave travelling along –x direction.
$Speed\ of\ wave\ = \frac{\omega}{k} = \frac{\sqrt{b}}{\sqrt{a}} = \sqrt{\frac{b}{a}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.