A0 and A1 coupling, arching, rib height, and f-hole geometry dependence in the 2 degree-of-freedom network model of violin cavity modes
George Bissinger · The Journal of the Acoustical Society of America · 1998
Six free parameters in the 2 degree-of-freedom (2DOF) network model [E. A. G. Shaw, J. Acoust. Soc. Am. 87, 398–410 (1990)] for the A0 and A1 cavity modes of the violin were optimized by fitting a 64-measurement database of frequencies and upper-/lower-bout pressure ratios obtained by varying volumes of water in a rigid, zero-arch aluminum violin cavity surrogate with various orientations. The optimized 2DOF model predicts an A0 frequency dependence on cavity volume of f∼V−0.25, quite different from the Helmholtz value of V−0.50 but in excellent agreement with experiment, signaling substantial coupling between the A0 and A1 modes. After modifying the model to separate rib height and arching dependence, predicted frequencies and pressure ratios behaved similarly—all decreased with increasing rib height or arching—with the notable exception of A1 frequencies, which increased with arching. For 11 instruments ranging in size from a 1/16th size violin to violoncellos, the optimized 2DOF model predicted A0 frequencies consistently ∼11% higher than experiment; similarly A1 frequency predictions were 15% high. The effects of sliding, flipping or rotating the f-holes were also investigated.