The speed of light is about a million times faster in air than sound, we don't notice car headlamps changing colour!
With galaxies, it's different. All are moving very quickly. In fact, Hubble noticed that the light from the galaxies was red-shifted. Dark lines (signatures of elements) in light waves are shifted towards the red end of the spectrum:
Red is a longer wavelength of light, so the frequency is less. This means that the galaxies must all be moving away from us.
Some nearby galaxies are blue-shifted. This means that they are moving towards us. Don't panic: we won't collide for a few billion years!