Inclusion of wave steepening in a frequency-domain model of trombone sound production

A frequency-domain model of trombone sound production that includes the effects of wave steepening is proposed. This model builds upon the work of Msallam et al. @Proceedings of the Institute of Acoustics 19~5!, 419–424 ~1997!# by including thermoviscous wall losses in a more realistic manner, by applying wave steepening systematically to the entire instrument, and by making quantitative comparisons to the experimentally measured output of the same trombone that the model is based on. The trombone is approximated as a set of contiguous cylindrical tubes with superposition of incoming and outgoing waves in each cylinder and with continuity of pressure and flow at each cylinder junction. The far-field radiated pressure spectrum is calculated on the basis of the spectrum of a measured pressure wave in the mouthpiece. This calculation includes the effects of wave steepening for the outgoing wave in each cylinder. The equations describing the model are given. Mouthpiece spectra are processed both with and without the effects of wave steepening. The predicted far-field spectra are compared to the corresponding measured far-field spectra. In all cases analyzed, the inclusion of wave steepening greatly reduces the error between predicted and measured spectra. © 2001 Acoustical Society of America. @DOI: 10.1121/1.1371759#