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While most ultrafast time-resolved optical pump-probe experiments in magnetic materials reveal the spatially homogeneous magnetization dynamics of ferromagnetic resonance (FMR), here we explore the magneto-elastic generation of GHz-to-THz frequency spin waves (exchange magnons). Using analytical magnon oscillator equations, we apply time-domain and frequency-domain approaches to quantify the results of ultrafast time-resolved optical pump-probe experiments in free-standing ferromagnetic thin films. Simulations show excellent agreement with the experiment, provide acoustic and magnetic (Gilbert) damping constants and highlight the role of symmetry-based selection rules in phonon-magnon interactions. The analysis is extended to hybrid multilayer structures to explore the limits of resonant phonon-magnon interactions up to THz frequencies.