Debye supposed that, in spite of its periodic nature, the crystal lattice can be represented by a continuum. By assuming suitable boundary conditions, he was able to show that there can only be certain modes of vibration for a given body; the situation is much the same as that which limits the number of stationary waveforms that are possible in a string that is stretched between two fixed points. The total number of possible modes in a continuum is really infinite but Debye considered only the 3N modes of lowest frequency, N being the number of atoms, since this leads to agreement with the classical expression for the specific heat at high temperatures. (Law of Dulong and Petit).

See Also

**Debye length**
**Debye length in a plasma**
**Debye length in an electrolyte**
**Law of Dulong and Petit**
**Mode**