Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

Analysis of the spheroidal modes of vibration of a free continuum elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively stark contrast between the two kinds of modes. Primarily transverse modes have a small divergence and have frequencies that are almost functionally independent of the longitudinal speed of sound. Analysis of inelastic light scattering intensity from confined acoustic phonons in nanoparticles requires an understanding of this qualitative distinction between different spheroidal modes. In addition, some common misconceptions about spheroidal modes are corrected.