Study on Nonlinear Acoustic Waves in Stepped Acoustic Resonators

The problem of investigating the nonlinear acoustic waves in stepped acoustic resonators is treated theoretically. A perturbation scheme that combines the method of multi-scale expansion yields a set of coupled nonlinear ordinary differential equations for deriving an analytical model to describe the resonant oscillations. The nonlinear sound pressure in stepped resonator is predicted with accuracy up to the second-order terms of a small-amplitude parameter epsilon. The pressure amplitudes and waveforms at the closed end of stepped resonators with different size parameters are investigated by the derived analytical model and qualitatively compared with the measured results in experiment. The qualitative comparison of calculated and measured results shows good agreement. The results suggest that the sound pressure generated in stepped resonators with different size parameters may be very different. Not all stepped resonators can generate high-amplitude and low-distortion standing waves. The derived analytical model can be used to qualitatively study the nonlinear acoustic waves in stepped acoustic resonators and design suitable tube dimensions for resonant macrosonic synthesis.