  Phonon measurements in the A15-type superconductors were complicated in the
past because of the unavailability of large single crystals for inelastic
neutron scattering, e.g., in the case of Nb$_3$Sn, or unfavorable neutron
scattering properties in the case of V$_3$Si. Hence, only few studies of the
lattice dynamical properties with momentum resolved methods were published, in
particular below the superconducting transition temperature $T_c$. Here, we
overcome these problems by employing inelastic x-ray scattering and report a
combined experimental and theoretical investigation of lattice dynamics in
V$_3$Si with the focus on the temperature-dependent properties of low-energy
acoustic phonon modes in several high-symmetry directions. We paid particular
attention to the evolution of the soft phonon mode of the structural phase
transition observed in our sample at $T_s=18.9\,\rm{K}$, i.e., just above the
measured superconducting phase transition at $T_c=16.8\,\rm{K}$. Theoretically,
we predict lattice dynamics including electron-phonon coupling based on
density-functional-perturbation theory and discuss the relevance of the soft
phonon mode with regard to the value of $T_c$. Furthermore, we explain
superconductivityinduced anomalies in the lineshape of several acoustic phonon
modes using a model proposed by Allen et al., [Phys. Rev. B 56, 5552 (1997)].
