Solving acoustic wave problems is one of the most important applications of the BEM, which can be used to predict sound fields for noise control in automobiles, airplanes, and many other consumer products. Acoustic waves often exist in an infinite medium outside a structure that is in vibration (a radiation problem) or impinged on by an incident wave (a scattering problem). With the BEM, only the boundary of the structure needs to be discretized. In addition, the BCs at infinity can be taken into account analytically in the BIE formulations, and thus these conditions are satisfied exactly. The governing equation for acoustic wave problems is the Helmholtz equation, which was solved using the BIE and BEM for more than four decades (see, e.g., some of the early work in Refs. [107–120]). Especially, the work by Burton and Miller in Ref. [108] is regarded as classical work that provides a very elegant way to overcome the so-called fictitious frequency difficulties existing in the conventional BIE for exterior acoustic wave problems. Burton and Miller's BIE formulation has been used by many others in their research on the BEM for acoustic problems (see, e.g., Refs. [50, 51, 121–125]).

The development of the fast multipole BEM for solving large-scale acoustic wave problems is perhaps the most important advance in the BEM that has made the BEM unmatched by other methods in modeling acoustic wave problems.