Volume 132, Issue 1, July 2012
Index of content:
- MUSIC AND MUSICAL INSTRUMENTS 
132(2012); http://dx.doi.org/10.1121/1.4726010View Description Hide Description
A hybrid, deterministic-statistical, parametric “dynamic filter” model of the violin’s radiativity profile [characterized by an averaged-over-sphere, mean-square radiativity ⟨R(ω)2⟩] is developed based on the premise that acoustic radiation depends on (1) how strongly it vibrates [characterized by the averaged-over-corpus, mean-square mobility ⟨Y(ω)2⟩] and (2) how effectively these vibrations are turned into sound, characterized by the radiation efficiency, which is proportional to ⟨R(ω)2⟩/⟨Y(ω)2⟩. Two plate mode frequencies were used to compute 1st corpus bending mode frequencies using empirical trend lines; these corpus bending modes in turn drive cavity volume flows to excite the two lowest cavity modes A0 and A1. All widely-separated, strongly-radiating corpus and cavity modes in the low frequency deterministic region are then parameterized in a dual-Helmholtz resonator model. Mid-high frequency statistical regions are parameterized with the aid of a distributed-excitation statistical mobility function (no bridge) to help extract bridge filter effects associated with (a) bridge rocking mode frequency changes and (b) bridge-corpus interactions from 14-violin-average, excited-via-bridge ⟨Y(ω)2⟩ and ⟨R(ω)2⟩. Deterministic-statistical regions are rejoined at ∼630 Hz in a mobility-radiativity “trough” where all violin quality classes had a common radiativity. Simulations indicate that typical plate tuning has a significantly weaker effect on radiativity profile trends than bridge tuning.