Measurements of frequency spectra of pressure along a wind-tunnel wall were made by single microphones and by a longitudinal array of four flush 0.8-inch circular microphones connected with alternating and with common phase. The alternating-phase array was designed to suppress by its wavenumber filtering the background acoustic duct noise at frequencies near 3 kHz. The measured levels set upper limits on low-wavenumber boundary-layer pressure. Analysis indicates that the high-wavenumber convective contribution in this frequency range was probably negligible, but it could not be definitely established whether background noise dominated the spectra or whether the upper bound set on low-wavenumber boundary-layer noise is a close one. On assumption of wavenumber independence in most of the pertinent low-wavenumber domain, an upper bound is given for the wavenumber spectral density of boundary-layer pressure, and its generalization is discussed. At lower frequencies, in identifiable domains where single-microphone and array spectra are dominated by the convective wavenumber component of boundary-layer pressure, satisfactory agreement is found with theoretical predictions based on current knowledge of the spectral density in the convective-wavenumber domain and ona measured facial sensitivity distribution for the microphone. In general, salient features of the array spectra correlate well with expectation, and the array technique is demonstrated to be a useful one for the subject purposes.