Could you please explain what exactly is the relevant information that is conveyed through a dispersion relation?
Edit 1: Sorry about being vague. I am currently trying to understand the dispersion relations obtained in the one-dimensional monoatomic and diatomic lattice and its relation to the optical and acoustic phonons. I understand how we arrived at the results, but I cannot fully visualize its implications from a physical point of view. I was hoping may be I can get some insight into the relations from a physical point of view.