Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to simplified calculations that assume isotropy. New low-frequency Raman light scattering data are presented for silicon spheres grown in a ${\mathrm{SiO}}_2$ glass matrix. Principal features of the Raman spectrum are not correctly described by a simple model of the nanoparticle as a free, isotropic sphere, but require both matrix effects and the anisotropy of the silicon to be taken into account. Libration, not vibration, is the dominant mechanism.