The lack of comprehensive literature on the all-important aspect of the elasticity of spinel ferrites led to the hydrothermal synthesis of different (Co, Zn, Ag) spinel ferrites. IR spectroscopy revealed the characteristic absorption bands of metal-oxygen in all three compositions. The shifting of tetrahedral and octahedral bending vibrations towards higher frequencies owes to changes in inter-atomic and inter-ionic distances. Elastic parameters, wave velocities, and Debye temperature have been calculated using IR spectroscopy data. Elastic parameters have been higher for Co ferrites than Zn and Ag ferrites. The Poisson ratio seems to be consistent for different spinel ferrites. Shear wave velocity has been found to be higher than longitudinal wave velocity because perpendicular particle vibrations take higher energy than parallel vibrations. Wave velocities have been found to be higher in Ag ferrites than in the other two compositions. Debye temperature follows the same trend as elastic parameters. Additionally, we have confirmed the mechanical stability of the Co, Zn, and Ag ferrites using the first-principles calculations in the density functional theory (DFT) approach framework. Interestingly, the Co/Zn/Ag ferrites exhibit semiconducting nature with a band gap of 3.96/3.66/0.71 ev. Our study could pave the way for next-generation spintronic devices.