Panels having enhanced, customizable acoustical characteristics are provided that comprise a core panel (12) of metal or bonded materials and that have an undulating exposed surface, with the size of the undulations being dependent on the wavelength of the sound intended to be diffused. The surface of the panel may also be provided with irregularities, such as perforations, for sound absorption, with the size, shape and layout of the irregularities being dependent on the wavelength of the sound intended to be absorbed. The core panel is combined with a backing matt (14) of bonded materials that is compression molded so as to have a density lower and thickness greater than that of the core panel. A film facing (16) may be applied to the front surface of the core panel, as well as an optional sound-transparent, aesthetic finish (18). The film facing may comprise a non-porous coating for high frequency diffusion applications.