Inclusion of wave steepening in a frequency-domain model of trombone soundproduction

A frequency-domain model of trombone sound production that includes the eff ects of wave steepening is proposed. This model builds upon the work of Msa llam ct al. [Proceedings of the Institute of Acoustics 19(5), 419-424 (1997 )] by including thermoviscous wall losses in a more realistic manner, by ap plying wave steepening systematically to the entire instrument, and by maki ng quantitative comparisons to the experimentally measured output of the sa me trombone that the model is based on. The trombone is approximated as a s et of contiguous cylindrical tubes with superposition of incoming and outgo ing 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. Mouthp iece spectra are processed both with and without the effects of wave steepe ning. The predicted far-field spectra are compared to the corresponding mea sured far-field spectra. In all cases analyzed, the inclusion of wave steep ening greatly reduces the error between predicted and measured spectra. (C) 2001 Acoustical Society of America.