Effect of tube dimensions on resonant frequency of stepped acoustic resonator

An investigation of the effects of tube dimensions on resonant frequencies of stepped acoustic resonators is conducted. A linear acoustic theory is employed to model the plane wave propagation in the stepped resonator. The linear eigenvalue problem obtained by the method of separation of variables is solved to derive a frequency equation. Then, an experimental apparatus is established, in which the tube dimensions can be changed to adjust frequency. The variation pattern of resonant frequency with different lengths and diameters of the sub-tubes is analyzed theoretically and experimentally. The results suggest that the overall length determines the approximate scope of the resonant frequencies while the exact values of resonant frequencies and the relationship between resonant frequencies of each mode are determined by the ratio of sub-tube lengths and the ratio of sub-tube diameters. The calculated results are compared with the measured data. The comparative research declares that the derived frequency equation is an effective tool to calculate the resonant frequency of stepped resonator with adjustable size used in wide-band microphone calibration.