Experimental characterization of basic violin structural acoustics

Abstract

Considering its simple construction the complex material-shape traditional violin, fashioned from nominally orthotropic materials to form a ported, compliant-wall cavity, enjoys a notable scientific complexity, e.g., four separate radiation mechanisms, coupling between the two lowest cavity modes A0 (Helmholtz resonance, ∼275 Hz) and A1 (1st longitudinal “slosh” mode, ∼470 Hz), and between A0 and two 1st corpus bending (B1) modes near 500 Hz. Comprehensive EMA (velocity/force), radiativity (pressure/force) and near-field acoustical holography ( f -hole volume flows/force) measurements plus bridge tuning systematics were combined to establish a dual-region structural acoustics model of the violin. In the “deterministic” region the large-volume-change B1 modes drive large, in-phase f-hole volume flows accounting for >50% of B1 radiation and excite A0; oppositely directed upper-bout/lower-bout cavity volume flows excite A1. A wall-driven, dual-Helmholtz resonator network successfully modeled A0 and B1 radiation. In the “statistical” region where the major bridge and plate tuning effects occur, radiation efficiency (averaged-over-sphere radiativity divided by averaged-over-corpus mobility) led to radiation damping and critical frequency. With total damping from mobility fits the radiation/total damping ratio (fraction of vibrational energy radiated) was combined with a parametric model of mobility. Splicing the regions created the “dynamic filter” model of violin radiation.Considering its simple construction the complex material-shape traditional violin, fashioned from nominally orthotropic materials to form a ported, compliant-wall cavity, enjoys a notable scientific complexity, e.g., four separate radiation mechanisms, coupling between the two lowest cavity modes A0 (Helmholtz resonance, ∼275 Hz) and A1 (1st longitudinal “slosh” mode, ∼470 Hz), and between A0 and two 1st corpus bending (B1) modes near 500 Hz. Comprehensive EMA (velocity/force), radiativity (pressure/force) and near-field acoustical holography ( f -hole volume flows/force) measurements plus bridge tuning systematics were combined to establish a dual-region structural acoustics model of the violin. In the “deterministic” region the large-volume-change B1 modes drive large, in-phase f-hole volume flows accounting for >50% of B1 radiation and excite A0; oppositely directed upper-bout/lower-bout cavity volume flows excite A1. A wall-driven, dual-Helmholtz resonator network successfully modeled A0 and B1 radiat...