The Violin as a Circuit

The paper applies elementary circuit ideas to bowed-string instruments and their component parts. Parameters are defined and calculations based on simple circuit diagrams for the main resonance and the air resonance; curves describe their combined performance. The relative importance of circuit resistances—wood loss, radiation, and wall-surface loss—is discussed. Wall-surface loss is an important component of air decrement. No material improvement is to be expected from change in decrement or enclosure volume. A theory for the wolfnote is given in terms of the beating of two equally forced oscillations, together with a criterion for its occurrence and a method for its elimination. The paper analyzes principles of dimensional scaling between members of the violin family and shows why the cello and viola are more susceptible to wolftone than the violin. A study of impedance requirements in wood shows that flexural similarity depends on the parameter c/ρ (compressional velocity over density); high values are in general favorable in the top plate. In the violin, cross-grain losses probably exceed those along the grain.