Physical modeling of wind instruments involving three-dimensional radiated sound fields

Abstract

For the Schumacher model and Adachi–Sato model, which are effective physical models of wind instruments, the present study introduces a more precise sound field expression using a three-dimensional wave equation, instead of one-dimensional analytical solutions of a wind instrument bore. The sound field around a bell section is expressed by the normally differentiated Kirchhoff–Huygens formula, then the boundary element method is applied to numerically analyze the formula. The remaining sound field inside the tube is analyzed with a conventional transfer matrix approach, and the two sound fields are coupled correctly, thereby modeling the total acoustic behavior of the wind instrument. The improved acoustic analysis method is combined with the Schumacher model and Adachi–Sato model to accomplish the physical modeling sound synthesis. Trial numerical calculations demonstrate that the developed method is effective in the sound synthesis of a clarinet and trumpet, involving three-dimensional characteristics of their radiated sound.