The utility of nanoscaled ferromagnetic particles requires both stabilized moments and maximized switching speeds. During reversal, the spatial modulation of the nanoparticle magnetization evolves in time, and the energy differences between each new configuration are accomodated by the absorption or emission spin waves with different wavelengths and energy profiles. The switching speed is limited by how quickly this spin wave energy is dissipated. We present here the first observation of dispersing spin waves in a nanoscaled system, using neutron scattering to detect spin waves in the CoO shells of exchange biased Co core- CoO shell nanoparticles. Their dispersion is little affected by finite size effects, but the spectral weight shifts to energies and wave vectors which increase with decreasing system size. Core-shell coupling leads to a substantial enhancement of the CoO spin wave population above its conventional thermal level, suggesting a new mechanism for dissipating core switching energy.