I have a question about Debye theory. In the book, we insert a factor of 3 into the density of states of phonons, for the three possible polarisations the phonons can have.
If we were to do Debye theory on a physical one-dimensional chain, would we use 3 polarisations also, due to the transverse oscillations the chain can have?
Am I correct in thinking the system would have only one acoustic mode - corresponding to the longitudinal motions along the chain?
Also, in a 3D crystal, when we speak of 3 acoustic branches, wouldn't these branches be degenerate & overlapping, having the same speed of sound?
I'm asking these questions whilst being a little confused over Q2 on the 2009 B2 paper, regarding acoustic modes.