Question

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

• A. $[LT]$
• B. $[T]$
• C. $[T^{-1}]$
• D. $[T^{2}]$

Answer 1

Answer: (B)

$\omega\left[\frac{x}{v}-k\right]$ is dimensionless and unit of $\frac{x}{v}$ is same as $k$ .
So, dimensions of $k=\frac{\left[x\right]}{\left[v\right]}=\frac{\left[L\right]}{\left[LT^{-1}\right]}=\left[T\right]$