Computer simulation of a trumpet

Abstract

In an effort to generate realistic trumpet mouthpiece pressure waveforms, a player-trumpet model was created that consisted of the player's lungs, the player's airway, the player's upper lip, and the trumpet. The player's lungs were modeled as a constant pressure source. The player's airway (from lungs to lips) was modeled as a resistance of 20 acoustic ω (cgs). The player's lip was modeled as a swinging-sliding door having 1 deg of rotational freedom and one degree of translational freedom. The trumpet was modeled in terms of its pressure response to a volume-flow impulse. Equations were solved iteratively to give (1) lip opening as a dynamic function of the forces and torques acting on the lip, (2) volume flow as a function of lip opening and the pressure difference across the lips, and (3) mouthpiece pressure as a convolution of volume flow with trumpet impulse response. Waveforms were calculated and displayed for the lip-opening area, the volume flow through the lips, and the pressure in the mouthpiece. The lip-opening area and mouthpiece pressure waveforms were realistic when compared to experimental waveforms in the literature. However, there are still too few experimental data to constrain the model in terms of lip closure time and total air flow on sustained notes. Simulation data will be presented and compared with experimental data. [The work to be reported was carried out while the author was on leave at IRCAM in Paris. René Caussé supplied player and trumpet data and Duanne Dudley supplied trumpet impulse data.]