Experiments have been conducted to study the propagation of sound over a rigid surface with a step discontinuity. The Biot–Tolstoy–Medwin (BTM) model of a rigid wedge [J. Acoust. Soc. Am.69, 1060–1064 (1981)] is used to predict the acoustic field directly in the time domain. Experiments carried out with a transient acoustic spark source confirm that: (1) in the region where there are no direct reflected waves, diffracted waves combine with diffracted/reflected waves to produce a smooth transition; (2) the acoustic field around the step discontinuity can be highly directional due to the interference of the direct, the reflected, the diffracted, and the diffracted/reflected waves; and (3) the acoustic field is essentially unchanged if the step discontinuity is replaced with a smooth step whose radius of curvature is less than the characteristic wavelength of the incident sound.