Question

The equation of a wave is given by $Y=A\sin$ $\omega (\frac{x}{v}-k)$, where $\omega$ is the angular velocity and $v$ is the linear velocity. Find the dimension of $k$?

Answer 1

Unit of $\frac{x}{v}$ is $\frac{M}{{MS}^{-1}}=S^{-1}=\left[T^{-1}\right]$

Unit of $k$ is same as $\frac{x}{v}$. So, unit of $k=\left[T^{-1}\right]$.