Blundell Thermal Physics · Problem 24.4

Phonons

Physics — Statistical Mechanics · phonon-density-of-states-linear-chain

Problem

Show that the density of states of lattice vibrations on a monatomic linear chain (see Section 24.3) is given by

g(\omega) = (2L/\pi a)[4K/m - \omega^2]^{-1/2}

. Sketch

g(\omega)

and comment on the singularity at

\omega = \sqrt{4K/m}