Accurate knowledge of the speed of sound is essential for acoustic modelling, since variations in this parameter influence wave propagation and system frequency responses. This study presents an FRF-based approach for estimating sound-speed variations within a finite element framework. Acoustic cavities are modelled using a Galerkin formulation, and the sound speed is identified through model updating by minimizing discrepancies between the FRFs of the reference and modified cavities. A new sensitivity equation, specifically derived for the speed-of-sound parameter, is introduced and incorporated into the updating procedure as a key methodological contribution. The approach is evaluated using two-dimensional and three-dimensional rectangular air-filled cavities with an admittance boundary. In both cases, the speed of sound is increased relative to its reference value, while 5% noise is additionally introduced into the three-dimensional FRF data. The updated models show close agreement with the FRFs of the modified cavities and reproduce their main resonant features. These results demonstrate the potential of FRF data, supported by the proposed sensitivity formulation, for estimating sound-speed variations without requiring separate propagation-time or wavelength measurements.