The Banjo: The “Model” Instrument

Abstract

At its lowest level of abstraction, the “simplified” banjo shown above is basically two interacting vibrating systems: a plucked string and a circular membrane. By “interacting” I mean that waves in the string generate waves in the membrane, and visa versa, so that the whole instrument vibrates together. The five-string banjo is a little more complicated as it has six interacting systems -five strings and one membrane. The equations which describe the way waves travel in these systems, how they radiate sound, and how they interact are fairly straightforward. For example, a string has only two coordinates, position and time, and the equation which describes the propagation of a disturbance along the string, the wave equation, links these two variables in such a way that if you know the wave’s position at any time, you know it at any time. It’s an analogous situation in the membrane but complicated somewhat by the bridge being placed away from the the membrane’s geometric center.