The electric field of an electromagnetic wave travelling through vacuum is given by the equation $E=E_0\sin \left(kx-\omega t\right)$. The quantity that is independent of wavelength is

The angular frequency ω is given by $\mathrm{\omega } = 2\mathrm{\pi }\nu$. 
The frequency of a wave varies with the wavelength. So, angular frequency is dependent on wavelength.

Now, $\mathrm{k}=\frac{2\mathrm{\pi }}{\mathrm{\lambda }}, \mathrm{\omega }=2\mathrm{\pi }\nu$

$\therefore \frac{k}{\omega }=\frac{2\pi /\lambda }{2\pi v}=\frac{1}{v\lambda }=\frac{1}{c}$

where $c$ is the speed of electromagnetic wave in vacuum. It is a constant whose value is $3 \times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}.$