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

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,
$v=\frac{\omega }{k}=\frac{100}{0.05}=2\times {10}^3\text{m/s}$