Time-domain numerical simulation of nonlinear wave propagation in a finite exponential horn

Finite-amplitude acoustic propagation in a finite exponential horn is numerically studied, with the reflected sound waves being taken into account. A quasi-one-dimensional nonlinear model is solved by high-order low-dispersion numerical schemes. In order to consider the broadband characteristics caused by nonlinear distortion of finite-amplitude waves, broadband time-domain impedance boundary conditions are used at the horn mouth. The impedance is expressed in the mathematical form of a partial fraction expansion with residues and poles, so that its time-domain equivalent can be calculated by efficient and causal recursive convolution. Good agreements between the experimental and numerical results of weak nonlinear propagation in a finite exponential horn are obtained. The present method can also be applied to predict the nonlinear wave propagation with distortion in a horn of arbitrary profiles.