Does speed of light depend on the wavelength or frequency of it?

[nineteen]

I heard that the speed of light doesn't depend on the wavelength or frequency of it, how does it happen? I don't understand it because the ultimate equation is c = fλ (where c is the speed of velocity of light, f is the frequency and λ is the wavelength of it...).

 

[Nugatory]

As the frequency increases the wavelength decreases, so their product doesn’t change.

 

[Ibix]

I heard that the speed of light doesn't depend on the wavelength or frequency of it

Where did you hear this? It's wrong in general.

The speed of light is a constant in vacuum. There isn't really an answer to why that is at a B level - it's just the way the world works. In terms of your $c=f\lambda$, it means that a light wave of frequency $f$ must have wavelength $c/f$. You don't get to choose both $f$ and $\lambda$.

For light in a medium, such as glass or water, the speed of light does vary with frequency. But again, this means that once you've chosen a frequency and a medium the wavelength is fixed, because you are not free to choose the speed and the frequency independently.