Question

Let a wave be described by the equation
$y=asin\omega \left(\frac{x}{v} - k\right)$
where, $\omega $ is angular velocity and $v$ is the linear velocity. What will be the dimensions of $k?$

• A. $\left[T^{2}\right]$
• B. $\left[T^{- 1}\right]$
• C. $\left[T\right]$
• D. $\left[L T\right]$

Answer 1

Answer: (C)

$y=asin\left(\frac{\omega x}{v} - \omega k\right)$
Angle is dimensionless, so
$\left[\omega k\right]=M^{0}L^{0}T^{0}$
i.e. $\left[k\right]=\frac{1}{\left[\omega \right]}=\frac{1}{T^{- 1}}=T$