Influence of tube geometry on the performance of standing-wave acoustic resonators

A general and simple calculation method is presented to investigate the effects of tube shape on the resonant frequency and performance of a resonator. First, the resonant frequency of a variable cross-section resonator is modeled using a transfer matrix. Then, the amplification ratio of the pressure amplitude (ARPA), defined as the ratio of the pressure amplitude at the small end to that at the large end of the resonator, is used to evaluate its performance. The ARPA value for a variable cross-section resonator can be directly calculated from its resonant frequency. It is shown that the ARPA value is closely related to the compression ratio. However, its value is only determined by the resonator itself and is independent of the working conditions. Therefore, the ARPA index is potentially a more convenient tool for evaluating the performance of resonators compared with other indexes. Additionally, the presented method is validated by a comparison with analytical results and experimental data. Moreover, the harmonic frequencies for cylindrical, exponential, conical, half-cosine, 3/4 cosine, and Horn-Cone shape tubes are numerically investigated, in addition to the influence of the resonator shape on the resonance frequency and ARPA. Finally, optimal shape parameters for several types of resonators are suggested.