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

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