This article documents some experimental observations made for near-exit unsteady pressure fluctuations in high-speed jets. These fluctuations are apparently related to ‘trapped waves’ within the jet potential core as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of three different aspect ratios are studied. The pressure fluctuations manifest as a series of peaks in the spectra. These ‘trapped wave spectral peaks’ are found with all nozzles. Their characteristics and variations with axial and radial distances as well as with jet Mach number are documented. Effects of initial boundary layer state and the presence of a surface nearby as well as the scaling of the frequencies of the spectral peaks are studied and discussed.