The propagation models for musical wind instruments are generally based on the assumption that a one-dimensional description is sufficient to describe the behavior of sound waves regardless of the geometry of the resonator axis. However, when the resonators are not straight, this description is not exact and modal approaches have shown that the pressure field has no symmetry in curved ducts, both in linear and weakly nonlinear propagation. The aim of the present study is to discuss the dynamics of nonlinear sound propagation in U-shaped ducts with geometries close to some parts of brass instruments resonators, in particular when the pressure level is so high that shock waves appear, as it is the case for brassy sounds. For this purpose, both experiments and numerical simulations in time domain have been performed. The experiments are based on optical measurements requiring a square section of the U-shaped portion of the duct. Numerical simulations have been performed by solving the 2D Euler equations in curvilinear coordinates using a finite-difference time-domain approach. Results reveal the dynamics of shock propagation and show nonlinear phenomena that are not yet taken into account when modelling nonlinear propagation of sound waves in brass instruments resonators.
