The banjo: Developing a plausible model from first principles.
Joe Dickey · The Journal of the Acoustical Society of America · 2010
The banjo is one of the few musical instruments which is amenable to analytical modeling. It is fundamentally two connected canonical wave bearing systems, and as such, it can be solved. Furthermore, the requisite computer code runs quickly, making it practical to examine the instrument’s response as functions of a variety of parameters. The parameters are the things banjo players tweek in their attempt to get the sound they want; things like head tension, bridge mass, and string gauge. This tutorial will start with first principles in both the physics and the mathematics and end with movies of the calculated head response and radiated sound as functions of time and frequency. Numerical models can never be exact. Real systems, and particularly musical instruments, are just too complex for this, but models can provide useful guidance by illuminating what might happen as parameters are changed.