  We theoretically study the modification of the energy spectrum of
long-wavelength acoustic phonons due to the electron-phonon interaction in a
three-dimensional topological Weyl semimetal under the influence of quantizing
magnetic fields. We find that the dispersion and attenuation of phonons show
striking oscillatory behaviors as varying the magnetic field at low
temperatures. These oscillations are distinct when the Fermi energy is in
different energy regimes. Moreover, the van Hove singularity of the Weyl
spectrum can manifest as a transition between different oscillation patterns
when increasing the magnetic field. These phonon behaviors could provide
testable fingerprints of the Fermi surface morphology and relativistic feature
of the Weyl semimetal.
