Waveguide Modeling of Lossy Flared Acoustic Pipes: Derivation of a Kelly-Lochbaum Structure for Real-Time Simulations

This paper deals with the theory and application of waveguide modeling of lossy flared acoustic pipes. The novelty lies in a refined 1D-acoustic model: the Webster-Lokshin equation. This model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross section, visco-thermal losses at the walls, and without assuming plane waves or spherical waves. Solving this model for a section of pipe leads to a quadripole made of four transfer functions which imitate the global acoustic effects. Moreover, defining progressive waves and introducing some "relevant" physical interpretations enable the isolation of elementary transfer functions associated with elementary acoustic effects. From this decomposition, a standard Kelly-Lochbaum structure is recovered and efficient low-cost digital simulations are obtained. Thus, this work improves the realism of the sound synthesis of wind instruments, while it preserves waveguide techniques which only involve delay lines and digital filters.