Computed cavity-air modes of Le Gruere violin and coupling to corpus modes

The internal cavity air modes of both a normal arched violin with f-holes and Calrleen Hutchin’s Le Gruyère violin with additional holes around the ribs have been computed using COMSOL MULTIDISCIPLINARY ACOUSTICS software. The calculations underpin the need to take finite size corrections into account when evaluating the acoustically important Helmholtz or A0 air resonance. The computed modal shapes and frequencies are compared with the assumptions and predictions of the Shaw two degrees of freedom network model. This has been widely used to interpret the dependence of the A0 and A1 resonant frequencies on both cavity volume and the number of additional holes opened around the ribs. Finite size effects are shown to have a marked influence on such dependencies. They are shown to result in marked deviations from predictions based on an ideal Helmholtz resonator. The coupling of the air modes to the corpus modes that excite them is considered using a simple dynamic model. The pedictions of the model are compared with those of the Shaw network model and measurements of the dependence of A0 and A1 mode frequencies on the number and placing of additional holes opened around the ribs of the Le Gruyère violin.