We focus our measurements on the acoustic phonons and not the optical phonons previously reported to exist for energies above $\sim$ 10 meV using optical techniques. [@Popovic03; @Jung08] We will show that there exists a range of acoustic phonon wavelengths associated with the $(C_{11}-C_{12})/2$ elastic constant where the TA mode both softens in energy and also increases in linewidth indicative of decreased lifetime.

This paper is divided into three main sections including this introduction. We first describe the neutron scattering experiments studying the low energy acoustic phonons where the softening in energy over intermediate wavevectors and then the linewidth broadening indicative of a shortening of phonon lifetimes is described. We finally conclude with a discussion comparing our results to theories for soft modes in Jahn-Teller systems and also a comparison between the anomalies observed here and in metallic systems with acoustic instabilities.

 \[sec:exp\] Experiments 
=========================

 \[sec:char\] Sample characterisation 
--------------------------------------

Three cylindrical single-crystals of [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{}, each of about 2 cm height and 0.75 cm diameter were grown using a mirror image furnace. Characterisation was performed using bulk susceptibility measurements and neutron diffraction confirming the presence of both a magnetic and structural transition. The bulk measurements of the heat capacity and the 