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Q.
A wave is expressed by the equation $y=0.5 \sin \pi(0.01 x-3 t)$, where $x, y$ are in metres and $t$ in seconds. The speed of propagation will be
AMUAMU 2000
Solution:
The standard equation of wave of amplitude $a$ is
$y=a \sin (k x-\omega t)$ ... (i)
where $\omega$ is angular velocity.
Given equation is
$y=0.5 \sin (0.01 \pi x-3 \pi t)$...(ii)
Comparing Eqs. (i) and (ii), we get
$k=0.01 \pi, \omega=3 \pi$
$k=\frac{\omega}{v} $
$\Rightarrow v=\frac{\omega}{k}=\frac{3 \pi}{0.01 \pi}=300 \,m / s$