and $d_{yz}$ orbitals, to best reproduce their experimental data for [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{}. The interplay between lattice and spin/orbital ordering was studied in [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{} by Watanabe *et al.* [@Watanabe14] using ultrasound measurements. They found that the $C_{11}$ and $C_{44}$ elastic constants show a softening region for cooling towards $T_{OO}$ and a large discontinuity at $T_{OO}$, which indeed suggests that there is a strong coupling between the orbitals of the Jahn-Teller ions and the lattice strain. In addition, Watanabe *et al.* [@Watanabe14] found a sensitivity of $C_{11}$ and $C_{44}$ on external magnetic fields up to 7 T in the \[110\] direction for the softening region near $T > T_{OO}$ in contrast to $\left(C_{11}-C_{12}\right)/2$, which does not depend on field.

In this work we present results of inelastic neutron scattering experiments above and below the orbital-ordering temperature $T_{OO}$ that yield the dispersion of the acoustic phonon branches in [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{} thus complementing the $q \rightarrow 0$ results of Watanabe *et al.* [@Watanabe14] Unlike ultrasound measurements which probe acoustic fluctuations in the $lim_{q \rightarrow 0}$ and Raman spectroscopy which is a strictly $q=0$ probe, neutron spectroscopy can investigate excitations associated with a uniform lattice deformation at all wavevectors, and hence wavelengths, over the entire Brillouin zone. 