The operation of a multitube pulse detonation combustor (PDC) evokes undesirable pressure fluctuations for a turbine downstream of the combustor. Pressure measurements in a downstream annular plenum reveal distinct pressure fluctuations. Although pressure peaks due to the shock waves emanating from the PDC tubes have been investigated in previous studies, pressure oscillations throughout the remaining cycle duration have received far less attention. Based on azimuthal and frequency mode decomposition of pressure signals at six circumferential positions, these oscillations are found to result from acoustic modes that are excited by PDC operation. This conclusion is verified by comparison with numerically calculated eigenmodes of the plenum. The impact of different operating parameters and the plenum outlet geometry on the acoustic oscillations are determined. The sequential firing of the PDC tubes at the lowest firing frequency in combination with a small blockage ratio was identified as the favorable configuration for the smallest acoustic fluctuations.