Thanks so would the conclusion be:
in a 1d lattice, nothing propagates faster than the maximum phase speed of the dispersion relation. Motion faster than this speed cannot be modeled by such as system without nonlinearity
I am struggling to understand shocks in a one dimensional lattice with a linear spring connecting the masses. Say I have a one dimensional lattice with a linear spring constant, k and lattice spacing a. If the particles in the lattice has mass, m then my speed of sound c is a*sqrt(k/m). That is...