The Debye model treats atomic vibrations as phonons in a box (the box being the solid). ... The approximation that the frequency is inversely proportional to the wavelength (giving a constant speed of sound) is good for low-energy phonons but not for high-energy phonons (see the article on phonons.)

What is Debye theory?

A theory of the specific heat capacity of solids put forward by Peter Debye in 1912, in which it was assumed that the specific heat is a consequence of the vibrations of the atoms of the lattice of the solid. ... The Debye temperature is characteristic of a particular solid.

What are Debye assumptions?

The Debye model assumes that the phonon density of states follows a parabolic, i.e. monotonously increasing, dependence of the fundamental frequency of lattice oscillations. This is a consequence of the approximation of the crystal lattice as an isotropic medium.