Acoustic cavity modes of a conventional and Le Gruyère violin
Colin E Gough · Proceedings of meetings on acoustics · 2010
The cavity air modes of both an arched violin with f-holes and Hutchin's Le Gruyère violin with additional holes around the ribs have been computed using COMSOL multi-disciplinary acoustics software. The computed modal shapes and frequencies are compared with the assumptions and predictions of the Shaw 2-degrees of freedom network model, previously 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 result in marked deviations of both the frequencies and internal acoustic pressures of the resulting independent a0 and a1 normal modes, which are more accurately described by the 3-dimensional computations and a linear acoustic transmission line model. An analytic model is introduced to illustrate the coupling of the air modes to the corpus shell modes and compared with the predictions of both 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.