Banjo Drum Physics - theoretical preliminaries

TL;DR

This paper presents a simplified theoretical analysis of the interaction between a banjo's drum head and enclosed air, highlighting how air resonances influence the instrument's timbre through wave mechanics.

Contribution

It introduces a basic wave mechanics model to analyze air-head interactions and quantifies how internal air resonances affect the drum head response.

Findings

Air resonances enhance the drum head response at specific frequencies

The air-head impedance mismatch allows treating the head as a driver of air

The analysis provides a quantitative understanding of timbre-related effects

Abstract

The interaction of a drum's head with its enclosed air is presented in the simplest possible form appropriate to the questions and issues that arise in understanding the timbre of the banjo. The inherent air-head impedance mismatch allows treating the head as driver of the air and the air's effect, in turn, as back reaction. Any particular question can then be addressed with a calculation in simple wave mechanics. The analysis confirms and quantifies the notion that internal air resonances enhance the response of the head at its and their frequencies. However, the details of just how are fairly complicated.