Question

A travelling wave pulse is given by $y=\frac{4}{3 x^{2} + 48 t^{2} + 24 x t + 2}$ where $x$ and $y$ are in metre and $t$ is in second. The speed of wave in $ms^{- 1}$ is :-

Answer 1

$y=\frac{4}{3 x^{2} + 48 t^{2} + 24 x t + 2}$
$=\frac{4}{3 \left[x^{2} + 16 t^{2} + 8 x t\right] + 2}$
$y=\frac{4}{3 \left(x + 4 t\right)^{2} + 2}$
here the value of, $\omega =4$ unit & $k=1$ unit
then wave speed,
$v=\frac{\omega }{k}=\frac{4}{1}=4\,ms^{- 1}$