  We report neutron inelastic scattering experiments on single crystal
PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ doped with 32\% PbTiO$_{3}$, a relaxor
ferroelectric that lies close to the morphotropic phase boundary. When cooled
under an electric field $\mathbf{E} \parallel$ [001] into tetragonal and
monoclinic phases, the scattering cross section from transverse acoustic (TA)
phonons polarized parallel to $\mathbf{E}$ weakens and shifts to higher energy
relative to that under zero-field-cooled conditions. Likewise, the scattering
cross section from transverse optic (TO) phonons polarized parallel to
$\mathbf{E}$ weakens for energy transfers $4 \leq \hbar \omega \leq 9$ meV.
However, TA and TO phonons polarized perpendicular to $\mathbf{E}$ show no
change. This anisotropic field response is similar to that of the diffuse
scattering cross section, which, as previously reported, is suppressed when
polarized parallel to $\mathbf{E}$, but not when polarized perpendicular to
$\mathbf{E}$. Our findings suggest that the lattice dynamics and dynamic
short-range polar correlations that give rise to the diffuse scattering are
coupled.
