Separability of wave solutions in nonlinear brass instrument modelling

Travelling wave representations of wave propagation are commonly employed in brass instrument modeling and have been extended to the nonlinear regimes. For the case of a real brass instrument, the assumptions that lead to the travelling wave solutions no longer strictly hold. The validity of these assumptions is investigated here with regard to two typical parts of brass instrument geometry. The first example shows that there is a small interaction between forwards and backwards travelling waves in a cylindrical tube. The second example highlights nonlinear backscattering of a traveling wave caused by variations in the tube cross-sectional area.