Extensive experimental studies of the coherently forward scattered sound at grazing incidence to low roughness rigid surfaces with periodic steep‐sloped elements have confirmed several of the theoretical predictions of large boundary wave amplitude and subsonic dispersion [Tolstoy, J. Acoust. Soc. Am.75, 1–22 (1984)]. For example, at short ranges the boundary wave amplitude diverges cylindrically and is proportional to εk3/2r−1/2, where ε is the scattering parameter,kis the wavenumber, andris the range; thereby, at sufficient ranges and frequencies it exceeds the amplitude of the spherically diverging direct wave. The dispersion is subsonic and goes asAk2ε2, whereAdepends on the roughness element. The experiments have also revealed an attenuation factor exp (−δr), where δ=αk6due to incoherent scatter up to critical rangekr=π/(Ak2ε2) beyond which an attenuation of form exp (− 1/2A2ε4k6r2) becomes dominant. This leads to frequency‐independent peak amplitudes two to six times the direct wave amplitude for the surfaces studied. Beyond this critical, frequency‐dependent, range the boundary wave catastrophically self‐destructs due to interference. The amplitude, dispersion, and attenuation of the boundary wave is a function of the packing, heights, and slopes or shapes of the scattering elements. Results are presented for spheres, spaced and packed circular cylinders, and several wedge corrugated roughness elements. The boundary wave is also shown to diffract over a ridge in the same manner as the direct wave from a point source.