Question

The equation of .a wave, travelling with amplitude A, linear u, angular velocity $\omega$ is given by
$y=Asin\omega (\frac{x}{v}-k)$
The dimensions of 'k' are

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

Answer 1

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

From the principle of homogeneity of dimension, two- quantities can be subtracted, if they have the same dimensions, hence k has dimensions similar to that of $\frac{X}{V}$.
$\therefore \frac{X}{V}=\frac{\left[L\right]}{\left[L{T}^{-1}\right]}=\left[T\right]=k$