Things I learned while teaching a graduate level course on the acoustics of musical instruments

Abstract

In spring 2013, I taught a graduate level course on the acoustics of musical instruments. A prerequisite of two courses on the fundamentals of acoustics and vibration allowed us to explore details and mathematical complexities. Due to time constraints and the decision to delve deep into details rather than provide a broad overview, the course focused on wind and stringed instruments. Both types of instruments were explored through the generator-resonator-radiator paradigm. We discussed nonlinear generators for winds (lip reed, mechanical reed, and air-reed) and realistic initial conditions for strings (finger plucked, struck by a nonlinear hammer, and the stick-slip bowing action); realistic resonators for winds (input impedance and the effects of holes, horns, and viscous losses) and strings (realistic boundary conditions and coupled motion); and radiation (bells and soundboards). This paper will describe some of the Mathematica animations used to illustrate the effect of tone holes on the input impedance of a woodwind instrument, the effect of mouthpiece volume on the input impedance of brass instruments, and the motion of plucked, struck, and bowed strings. We will discuss the challenges of teaching a graduate level course, and what I would do differently the next time I teach it.