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Q.
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 velocity of wave is
Waves
Solution:
$y=\frac{4}{3 x^{2}+48 t^{2}+24 x t+2}$
We need to convert it into the form of $f(k x-\omega t)$
$y=\frac{4}{3\left(x^{2}+16 t^{2}+8 x\right)+2}$
$y=\frac{4}{3(x+4 t)^{2}+2} $
$v=\frac{\omega}{k}$
Hence $v=\frac{4}{1}=4 \,m / s$