An analysis is made of the sound produced during low Mach number turbulent flow over a roughened section of a nominally plane, rigid wall. The wall is roughened over a finite distance in the mean flow direction, and the roughness elements are modeled by a random distribution of hemispherical bosses. The individual bosses constitute surface inhomogeneities at which near field pressure fluctuations of the turbulence Reynolds stresses are diffracted into sound. Each boss is acoustically equivalent to a dipole source, and their collective radiation intensity is proportional to the sixth power of the mean flow velocity and the wetted area of the roughened section of the wall. Additional dipole sources of sound are located in the neighbourhoods of the boundaries of the roughened region. Experiment suggests that the strongest of these occur at the forward facing, smooth-torough transitiQn, where the boundary layer is displaced outwards from the wall. The noise generated there is equivalent to that produced by the same turbulence convecting over a forward facing step of rounded profile, and is predicted to exceed that from the distributed dipoles provided the roughness is confined to a region of moderate extent in the flow direction. The sound produced by a rounded forward facing step is also compared with that from a discontinuous step of the same height in the hypothetical case in which the turbulence Reynolds stress sources are the same.