A new algorithm to simulate nonlinear propagation in a tube of any shape. Application to a real-time physical model of trumpetlike instruments
Christophe Vergez, Xavier Rodet · The Journal of the Acoustical Society of America · 1999
When air pressure is low enough, wave propagation in a pipe can be considered linear to a reasonable degree. When the pressure level increases, this simplification becomes more and more inaccurate since high pressure values travel faster than low pressure values. The speed of propagation is thus a function of the pressure level. A new time-domain approach is proposed to simulate nonlinear propagation of a sound wave in a tube of any shape. This constraint-based algorithm does not prevent the derivative of the signal from breaking, as it happens when a shock wave occurs. Moreover, the algorithm allows the carrying out of nonlinear propagation even once a shock has occured. Thus, as expected the distorsion of a sinusoidal wave into a N-wave of progressively decreasing amplitude was observed. Moreover, without any additional computational cost, this technique provides fractional delay variation as needed for continuous tube’s variations in length. The nonlinear propagation algorithm is included in the real-time high-quality physical model of trumpetlike instruments. Simulation shows a great improvement in the sound quality since this algorithm allows subtle nuances in the timbre as well as hard brassy effects.