The destructive interferences observed in Excess Attenuation (EA) spectra over periodically and randomly spaced roughness elements with different cross-sectional profiles (semi-cylindrical, rectangular and wedge-shaped strips) have been investigated. If the roughness is spaced periodically, then two or three destructive interference maxima are observed in the same frequency range as the one or two observed with randomly distributed roughness. Roughness-induced surface waves are investigated also. Their amplitudes and the freq-uencies at which they occur are found to depend on the roughness height, mean center-to-center spacing and the extent to which the roughness is periodic. A semianalytical Multiple Scattering Theory and a numerical method (the Boundary Element Method) have been used to make predictions of the EA spectra which are compared with measurements. In addition it is found that the effective surface impedance spectra deduced from complex EA measurements over rough surfaces exhibit resonances similar to those observed for a hard-backed porous layer. On this basis a heuristic effective impedance model for rough hard surfaces is developed and the corresponding predictions of EA spectra are compared with data.