My book considers waves in crystals. Especially it develops the idea of acoustical and optical branches of the waves. From what I can see these are different ways the dispersion of our phonon may look like. It is developed when the crystal contains more than one atom per unit cell, but I am not sure why this is. Do we not have acoustical and optical branches for a wave in any crystal regardless of how many atoms we have per unit cell and what their mass ratio might be? Also I am not sure what dispersion even means. It is a relationship between the phase velocity and the wavelength (or wavevector k), but what is the physical meaning of this quantity. When a physicist describes different kinds of dispersion in a crystal is he then describing different forms of wavemotion that can occur in the crystal? Maybe my question is kind of confusing but I just want to clear up some things that my books explains quite poorly.