Acoustics of the banjo: theoretical and numerical modelling

A previous paper [Woodhouse et al., Acta Acustica 5, 15 (2021) https://doi.org/10.1051/aacus/2021009] showed acoustical measurements of an American 5-string banjo alongside similar measurements on a guitar, revealing a strong contrast in bridge admittance. Theoretical and numerical modelling is now presented to probe the physics behind this contrast. Without the bridge and strings, the banjo membrane has a rising trend of admittance associated with its modal density, and it has a distinctive pattern of sound radiation because an ideal membrane has no critical frequency. When the bridge and strings are added to the banjo, three formants shape the amplitude envelope of the admittance. One is associated with local effects of mass and stiffness near the bridge, and is sensitive to bridge mass and the break angle of the strings over the bridge. The other two formants are associated with dynamical behaviour of the bridge, analogous to the “bridge hill” in the violin.