A first-principles based investigation of influence of magnetism on lattice dynamics of Fe 72Pd 28 system near the Invar composition has been carried by computing the pressure dependence of the phonon frequencies, the Gru n ¨ eisen parameters, the disorder-induced widths and the elastic shear constant using a combination of transferable force constant model, density functional perturbation theory and the itinerant coherent potential approximation, an analytic tool for performing configuration averaging in disordered alloys. We find that with increasing pressure and collapse of magnetic moment, the TA 1[110] phonon frequencies harden along with the elastic shear constant. We do not observe any significant variation of the mode Gru n ¨ eisen parameter with change in magnetic moment. These results indicate that there is no magneto-volume effect on the lattice dynamics and the experimentally observed phonon softening with increasing magnetization has to be associated with the martensitic instability.