Is the relation c=νλ valid only for Electromagnetic waves?

Question

What is the validity of the relation $c = \nu\lambda$? More specifically, is this equation valid only for Electromagnetic waves?

I read this statement in a book, which says:

de Broglie waves are not electromagnetic in nature, because they do not arise out of accelerated charged particle.

This seems correct, but arises a doubt in my mind.
Suppose I find out the wavelength of a matter wave (or de Broglie wave) using de Broglie's wave equation: $$\lambda = \frac{h}{p}$$

Now, can I use $c = \nu\lambda$ to find out the frequency of the wave?

Answer 1

No.

The general relation is given by

$$v = \lambda\nu$$

Where $v$ is the velocity of the considered wave and $\lambda$ and $\nu$ its wavelength and frequency. Of course in the case of an electromagnetic wave which is traveling at the speed of light you gain

$$c = \lambda\nu$$

If you're treating instead some massive particle, then thou have $$p = \frac{Ev}{c^2}$$

and using $E = \frac{h}{\nu}$ you obtain $$p = \frac{h}{\lambda}$$

For a non-relativistic particle

$$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$$, where $K$ is the non-relativistic kinetic energy $K = \frac{p^2}{2m}$.