Triggering new stable macroscopic orders in materials by ultrafast optical or terahertz pump pulses is a difficult challenge, complicated by the interplay between multiscale microscopic mechanisms, and macroscopic excitation profiles in samples. In particular, the differences between the two types of excitations are still unclear. In this article, we compare the optical response on acoustic timescale of a V₂O₃ Paramagnetic Metallic (PM) thin film excited by a terahertz (THz) pump or an optical pump, at room temperature. We show that the penetration depth of the deposited energy has a strong influence on the shape of the optical transmission signal, consistent with the modulation of permittivity by the superposition of depth-dependent static strain, and dynamical strain waves travelling back and forth in the sample layer. In particular, the temporal modulation of the optical transmission directly reflects the excitation profile as a function of depth, as well as the sign of the acoustic reflection coefficient between the film and the substrate. The acoustic mismatch between the V₂O₃ layer and the substrate was also measured. The raw data were interpreted with a one-dimensional analytical model, using three fitting parameters only. These results are discussed in the context of triggering phase transitions by ultrafast pump pulses. To the best of our knowledge, this is the first report of the modulation of the optical transmission of V₂O₃ with a THz pump within the acoustic timescale.