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Understanding the occurrence of various feedback mechanisms of an under-expanded impinging supersonic jet is a crucial task in research. The presence of several jet modes is examined in this study for the flat and corrugated impinging plate geometries. The behavior of impinging plate configurations during mode switching is investigated by varying the flow state, such as the jet Mach number. The staging behavior at various jet Mach numbers is observed using acoustic spectral plots and schlieren flow visualization. To explore the presence of various types of modes during the jet impingement due to the modification of jet Mach number, ensemble averaging and Proper Orthogonal Decomposition of schlieren images are carried out. In the majority of situations, the corrugated design shows a reduction in tonal noise and overall sound pressure level. In exceptional cases, for the corrugated plates, the enhanced overall sound pressure level is caused by the existence of axisymmetric instability (A1, A2).