Time-averaged two-point measurements of the fluctuating wall pressure and instantaneous measurements of the full fluctuating wall pressure field were performed in incompressible turbulent impinging jets with nozzle-to-plate spacings of 2 and 4 diameters, Reynolds numbers of 23 300, and Mach numbers of 0.03. An azimuthal Fourier decomposition of the fluctuating wall pressure revealed that the fluctuations in the stagnation region were dominated by azimuthal mode 1 to 3, and the contributions from these modes were larger for the jet with $H/D=4$. Azimuthal modes 0 and 1 made significant contributions to the pressure fluctuations in the wall jet region of both jets, indicating that the large-scale ring structures formed in the jet shear-layer play a prominent role in this region. The contributions from modes 0 and 1 in the wall jet were smaller for the jet with $H/D=4$ indicating that the ring structures play a less prominent role in the wall jet region as the nozzle-to-plate distance increased. A wavelet analysis of the transient fluctuations indicated that azimuthal mode 1 had dominant high-frequency and low-frequency components, while azimuthal mode 0 had only the higher-frequency oscillations. The higher-frequency components of azimuthal modes 0 and 1 occurred in both the stagnation and the wall jet regions and are attributed to the asymmetric evolution of the ring structures in the jet. The low-frequency oscillations were primarily associated with azimuthal mode 1 and were evident only in the stagnation region. These oscillations became more prominent as the nozzle-to-plate distance was increased.