The displacement of a progressive wave is represented by $y = A \sin(\omega t - kx)$,where $x$ is distance and $t$ is time. Write the dimensional formula of $(i)$ $\omega$ and $(ii)$ $k$.

(N/A) The argument of the trigonometric function,$(\omega t - kx)$,must be dimensionless because the sine function is a dimensionless ratio.
$(i)$ For $\omega t$ to be dimensionless:
$[\omega][t] = [M^0 L^0 T^0]$
$[\omega][T] = [M^0 L^0 T^0]$
$[\omega] = [T^{-1}] = [M^0 L^0 T^{-1}]$
$(ii)$ For $kx$ to be dimensionless:
$[k][x] = [M^0 L^0 T^0]$
$[k][L] = [M^0 L^0 T^0]$
$[k] = [L^{-1}] = [M^0 L^{-1} T^0]$