The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D. / Most flows of practical interest are turbulent in nature, typically occurring next to a rigid surface such as a submarine hull or aircraft wing. This boundary layer flow is of engineering importance because its pressure fluctuations are the source of unwanted structural vibrations and undesired acoustic noise. From a purely scientific perspective, it is useful to study the turbulent pressure fluctuations in order to learn more about the workings of the region of the flow closest to the surface. Turbulent flow over smooth walls has been researched extensively. However, one cannot ignore the fact that surfaces of practical interest are not smooth. Thus, it is important to account for the effect of roughness on the turbulent boundary layer. It has been found that there are significantly greater pressure fluctuations over rough walls when compared to smooth walls. Consequently the extent of vibrations and noise which occur in rough walls is larger than that experienced in smooth walls. The present study seeks to shed light on the nature of the rough-wall turbulent boundary layer through wind tunnel experiments. The nature of the velocity, pressure fluctuations, and turbulence within the boundary layer are examined as well as the existence of universal relationships which are applicable to all rough-wall turbulent boundary layers. A method for predicting the pressure fluctuations (to within 4-dB) over a specific rough wall is also proposed.