Abstract:

A result of the Bloch theory is that the eigenstates of an electron in a strictly periodic potential are extended and the corresponding energy levels form clustered energy bands separated by gaps. In the study reported here, a finite air-filled tube with arbitrary mass density modulation which permits the inclusion of disorder in the study of the acoustic frequency bands is theoretically considered. Since the theoretical model is finite, direct comparisons can be made with the experiment. The baffled tube is excited with a sound source at one end. The source can deliver short pulses as well as harmonic oscillations. Both normal mode analysis (NMA) and pulse analysis (PA) have been used. The spectra obtained from both methods are compared with our theoretical prediction. For the tube with evenly spaced baffles, three passing frequency bands have been found. More interestingly, some localized resonant modes are discovered whose frequencies lie in the gaps. The wave functions of these modes are confined within a few sections of divided tube at both ends.