Acoustic phonon (${\omega }_{\mathbf{q}}\to 0\text{ as }q\to 0$)

An acoustic phonon is a quantum of vibration on an acoustic phonon branch. At long wavelengths the atoms in each primitive cell move together and translational invariance makes the frequency approach zero. A three-dimensional crystal has three acoustic branches, corresponding to longitudinal and transverse polarizations. A linear small-wavevector dispersion has slope equal to the appropriate sound speed.