Question

A travelling wave pulse is given by equation,
$y=\frac{4}{3x^2+48t^2+24xt+2}$, where $x$ and $y$ are in metre and $t$ is in second. The wave velocity is

• A. $4\text{m/s}$
• B. $3\text{m/s}$
• C. $2\text{m/s}$
• D. $1\text{m/s}$

Answer 1

The correct option is A $4\text{m/s}$

The given wave equation will represent a travelling wave, if $y=f(kx\pm \omega t)$
Given:
Wave equation,
$y=\frac{4}{3x^2+48t^2+24xt+2}$
$\Rightarrow y=\frac{4}{3(x^2+16t^2+8xt)+2}$
$\Rightarrow y=\frac{4}{3{(x+4t)}^2+2}$
On comparing with form, $y=f(kx\pm \omega t)$, we get,
$k=1$ and $\omega =4$
So, wave velocity
$v=\frac{\omega }{k}=\frac{4}{1}=4\text{m/s}$

Why this question? It tends to test the understanding of the fundamental format of a travelling wave.