  We study acoustic modes of a close-packed hexagonal lattice of spheres
adhered to a substrate, propagating along a high-symmetry direction. The model,
accounting for both normal and shear coupling between the spheres and between
the spheres and the substrate, yields three contact-based vibrational modes
involving both translational and rotational motion of the spheres. Furthermore,
we study the effect of sphere-substrate and sphere-sphere contacts on
spheroidal vibrational modes of the spheres within a perturbative approach. The
sphere-substrate interaction results in a frequency upshift for the modes
having a non-zero displacement at the contact point with the substrate.
Sphere-sphere interactions result in dispersion of spheroidal modes turning
them into propagating waves, albeit with a small group velocity. Analytical
dispersion relations for both contact-based and spheroidal modes are presented
and compared with results obtained for a square lattice.
