  Weyl semimetals display unusual electronic transport properties when placed
under magnetic fields. Here, we investigate how magnetic fields alter the
dynamics of long wavelength lattice vibrations in these materials. To that end,
we develop a theory for the phonon dispersion, which incorporates contributions
from chiral and nonchiral Landau levels, electron-phonon interactions,
electron-electron interactions, and disorder. We predict (i) a
magnetic-field-induced hybridization between optical phonons and plasmons, (ii)
avoided crossings between pseudoscalar optical phonons and electronic
excitations originating from nonchiral Landau levels, (iii) a sharp dependence
of the sound velocity on the relative angle between the sound propagation and
the magnetic field. We compare our results to recent theoretical studies on the
signatures of the chiral anomaly in phonon dynamics.
