Question

The equation of a wave is given by $y=asin\omega (\frac{x}{v}-k)$, where $\omega$ is angular velocity and $v$ is linear velocity. The dimensions of $K$ will be

• A. $\left[T^2\right]$
• B. $\left[T^{-2}\right]$
• C. $\left[T\right]$
• D. $\left[LT\right]$

Answer 1

The correct option is C $\left[T\right]$

The quantity $(\frac{\omega x}{v}-\omega k)$ inside the sine function has dimension of angle and hence $\omega k$ is dimensionless being angle.
But $\left[\omega \right]$ $=\left[T^{-1}\right]$, therefore $\left[k\right]=\left[T\right]$