Standing waves in air columns: Will computers reshape physics courses?

Abstract

It is often argued that the introduction of computational physics into undergraduate courses will, in time, change what is taught. This paper presents a supporting example, taken from the field of musical acoustics. The vibration of the air columns inside wind instruments, of any but the most idealized shapes, is a sufficiently difficult analytic problem that the subject is rarely treated in ordinary undergraduate courses. A simple computational treatment of the problem is presented that demonstrates many features of importance to real musicians: the effect of mouthpieces and bells, the positioning and sizing of fingerholes, and the production of multiphonics. The ability to treat previously intractable problems like this may enable acoustics to regain a place in the ordinary curriculum and allow its potential as an intuitive model for related systems to be usefully exploited.