Wave propagation in acoustic tubes forms the basis of musical sound production in wind and brass instruments, as well as in the case of the human voice. There are various ways of defining what is meant by the word ``tube." In general, it can be described as an enclosure for which the length scale in one coordinate is significantly greater than in the others. Generally, in linear problems, the dynamics of the material filling the tube (air in musical applications) will satisfy the wave equation, in three dimensions. If it is true that the wavelengths of interest are longer than the length scale in the two ``short" coordinate directions, then it is possible to simplify the dynamics to one dimension.
The simplest case of numerical methods for lossless cylindrical tubes is described by the 1D wave equation, which was covered in some depth in Chapter 6; it will thus be presented in an abbreviated form in §9.1. The more interesting case of the conical tube, of great interest wind instrument modelling, will be approached in §9.2. The coupling with models of toneholes and reeds is approached in §9.3 and §9.4, respectively. Finally, a general numerical model of the dynamics of acoustic tubes, described by Webster's equation is presented in §9.5.
References for this chapter include: [193,53,239,20,143,71,123,182,55,211,124,242,241,240,150]