Question

A standing wave is represented by $y=a\sin \left(0.05x\right)\cos \left(100t\right)$, where $t$ is in $\text{second}$ and $x,y$ are in $\text{meter}$, then the velocity of the constituent wave is

• A. ${10}^2\text{m/s}$
• B. ${10}^5\text{m/s}$
• C. ${10}^3\text{m/s}$
• D. $2\times {10}^3\text{m/s}$

Answer 1

The correct option is D $2\times {10}^3\text{m/s}$

Given:
$y=a\sin \left(0.05x\right)\cos \left(100t\right)$
On comparing with the equation of standing wave,
$y=2A\sin \left(kx\right)\cos \left(\omega t\right)$,
Wavenumber, $k=0.05{\text{m}}^{-1}$
Angular frequency, $\omega =100\text{rad/s}$
So, Velocity of constituent wave,
$v=\frac{\omega }{k}=\frac{100}{0.05}=2\times {10}^3\text{m/s}$