The banjo in the time-domain

Abstract

The banjo is under-represented in the musical acoustics literature. This is the case even though it is basically a vibrating and radiating membrane driven by a plucked string, and thereby lends itself naturally to modeling and analysis. A recent frequency domain model, [Dickey, J. Acoust. Soc. Am. 114, 2958–2966 (2003)] will be reviewed. The work reported here is a time domain analysis. First, the response of an isolated, plucked, lossy and dispersive string is presented. The string is then connected through a bridge to the center of a circular membrane. The string and head are treated as two fully connected dynamic systems and the response of the head is calculated. The isolated head is then driven off-center with an harmonic drive and the temporal response is determined by ray-tracing and summing amplitudes over a grid. Resonance frequencies and modal patterns agree well with experiment thereby validating the technique. Finally, the resonant string is considered as an external, transient, off-center and spatially distributed drive and the temporal response of the head is derived using the ray tracing technique. These modal patterns evolve in time and eventually stabilize to patterns that are in qualitative agreement with experiment.