Numerical verification of the existence of shock waves in trombones

The brassy timbre associated with loudly played trombone notes is due to the accumulated effects of nonlinear wave propagation. Hirschberg et al. experimentally showed in [J. Acoust. Soc. Am. 99, 1754–1758] that wave steepening of such tones can be strong enough to produce shock waves. In this paper, pressure measurements collected along the trombone bore are presented and then numerically simulated using a three-dimensional time-domain model. The numerical solutions reveal that shock waves do form within the computational instrument within the vicinity of the approximated shock distance.