Question

A wave equation which represents the displacement of particle along $y-$ axis is given as:
$y=10\sin \left(\right(30t-2x)+\frac{\pi }{4})$
where $x$ and $y$ are in meter and $t$ in $\text{sec}$. The velocity of wave is

• A. $10\text{m/s}$ along $+vex-$ axis
• B. $20\text{m/s}$ along $-vex-$ axis
• C. $15\text{m/s}$ along $+vex-$ axis
• D. $15\text{m/s}$ along $-vex-$ axis

Answer 1

The correct option is C $15\text{m/s}$ along $+vex-$ axis

$y=10\sin \left(\right(30t-2x)+\frac{\pi }{4})$
On comparing this equation with $y=A\sin (\omega t-kx+\varphi )$
we get $\omega =30\text{rad/s},k=2$
The wave velocity is,
$v=\frac{\omega }{k}$
$\Rightarrow v=\frac{30}{2}=15\text{m/s}$
As the given wave equation is of the form $A\sin (\omega t-kx+\varphi )$
Therefore the wave is propagating along $+vex-$axis direction.