Cavity resonance in the violin: Network representation and the effect of damped and undamped rib holes

Abstract

The upper and lower volumes of the violin cavity are treated as acoustical capacitances coupled by an internal inertance. This leads to the development of a simple acoustical network that takes into account the noncentral position of the f-hole system and has two degrees of freedom representing the Helmholtz mode A0 and the primary longitudinal mode A1. The initial choice of values for the network elements is based in part on wave-acoustical considerations. These values are then adjusted under the guidance of new experimental data. In particular, when the violin is operating in the A0 mode, it is found that the acoustic pressure in the upper volume is 30% greater than that in the lower volume. The presence of rib holes around the upper and lower volumes is represented by additional network elements shunting the acoustical capacitances. The characteristics of the modified instrument, with and without rib-hole damping, are presented in terms of the calculated values of the resonance frequencies ν0 and ν1 , the Q factors, and the volume velocity ratios (φ) of the A0 and A1 modes as functions of the number of rib holes. (The parameter φ provides an indication of the volume velocity passing through the rib holes in comparison with that associated with the f-hole system.) The calculated values are compared with experimental data for the special instrument known as ‘‘Le Gruyère’’ [C.M. Hutchins, J. Acoust. Soc. Am. Suppl. 1 73, S84(1983); 87, XXX–XXX (1990)].