Global modeling of the violin radiativity profile.

Abstract

The violin’s radiativity (pressure/force)profile maintains a consistent shape across quality classes, arguing for a quality‐independent generalized global model. In the 196–660 Hz region the lowest cavity modes A0 and A1 and the two first corpus bending modes B1 generate almost all the radiativity, with the B1 modes treated as “pumps” for A0 and A1. The B1 modes have nodal patterns similar to the plate bending (primarily) modes 2 and 5, suggesting a link to the violin’s critical frequency. The essentially serial character of the violin’s sound chain leads naturally to a simplified expression for the averaged‐over‐sphere radiativity profile as a product of just two filters: (1) string‐to‐corpus through the tuned bridge substructure “gatekeeper”) filter and (2) the “egress” filter for the vibration‐radiation transformation, the latter reliably parametrized by the radiation‐total damping ratio FRAD. FRAD incorporates the violin critical frequency as well as top and back plate properties in a generalized form. The gatekeeper filter on the other hand is considerably more complex; present bridge models must be augmented by systematic empirical measurements to understand the effects of varying bridge rocking mode frequency or “wing” mass. Recent three‐dimensional vibration measurements provide additional insight into bridge‐corpus impedance effects.