The Raman light to vibrations coupling coefficients C(ν) of quadrupolar and symmetrical vibrational modes of spherical nanoparticles embedded in a matrix are calculated. In contrast to the symmetrical mode, the C(ν) of the quadrupolar modes consists of the longitudinal and transversal sound velocity contributions. It is shown, that depending on the ratio of longitudinal and transverse sound velocity, these two contributions can interfere constructively or destructively resulting in enhancing or vanishing of some radial modes. Different peaks in the C(ν) spectrum were attributed to transverse and longitudinal spheroidal modes and the longitudinal spheroidal modes were found to have a higher Raman intensity than the transverse modes. The theoretical model was tested on a sample of HfO2 nanoparticles in a silica matrix.