Theoretical prediction and experimental modal analysis of sound propagation along a long enclosure

The acoustical properties of sound in a long rectangular enclosure with a circular loudspeaker mounted on the top wall of the duct end are investigated in the present study. A mathematical model of the pressure wave generated by assuming a flush-mounted circular piston vibration as the sound source in terms of the acoustic mode for a rigid duct is derived. Experiments are carried out to compare the theoretical predictions. A probe microphone is used to capture sound pressures across several enclosure cross sections and a reference signal obtained from a microphone fixed in position inside the enclosure provides the phase reference for the mode capturing. Results show that resonance frequencies do not appear in spanwise modes of odd number. Some acoustic modes with patterns similar to some degenerate modes of the rigidwall duct modes are identified. The presence of such degenerate mode is found to be due to air damping. Experimental observations are in line with the theoretical predictions.