A sound absorbing hollow core panel of structural material based on Helmholtz resonator properties consisting of two exterior skins connected by spacers or structural connections and bounded by perimeter skins or structural connections with internal cavity or cavities that communicate with the exterior sound field through a plurality of orifices in one or both exterior skins as well as the perimeter of the panel and that have a plurality of Helmoltz resonators of different shapes and sizes tuned to specific frequencies that control the sound absorption characteristics of the hollow core panel. The internal cavity or cavities are defined by external skins and perimeters as well as internal structural elements acting as interior dividers, interior sub-volumes and perimeter structures, each of which may contain a plurality of orifices for sound communication forming a sequence of first order Helmholtz acoustical resonators with respective natural frequencies for sound absorption. Panels may be assembled with or without selected interior elements or perimeter structures as a basis for infinite flexibility in building sound absorbing walls of selectable sound absorbing characteristics and size. The numbers and geometries of the orifices as well as the sizes of the internal cavities may be varied generally, thus adding to the flexibility of the invention. Sound dissipating material may also be incorporated in the cavities of the panel.