Question

The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$, where $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is (in $\text{m/s}$)

Answer 1

Given, equation of a plane progressive wave
$y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$
Comparing the above equation with,
$y=A\sin 2\pi (\frac{t}{T}-\frac{x}{\lambda })$
we get $\lambda =0.30\text{m},T=0.01\text{s}$
Hence velocity of propagation,
$v=\frac{\lambda }{T}=\frac{0.3}{0.01}$
$\Rightarrow v=30\text{m/s}$