Contemporary Generalized Normal Mode Violin Acoustics

摘要

The acoustic properties of a violin can be analyzed in terms of its normal modes by incorporating mode radiativity in addition to the usual vibratory properties. A normal mode database that includes qualitative evaluations as well lends itself to examining aspects of violin dynamics related to quality classes such as "good" or "bad", a relatively straightforward matter for violinists, but much more problematic scientifically. Since the low-lying "signature" modes have shown no robust quality differentiation, our normal mode acoustics investigations move to general aspects of violin acoustics using band-average and trendline quantifiers covering the entire sound spectrum. Initially, understanding the fundamental vibrational energy loss behaviors is of most interest. For a violin suspended "free-free" both total and radiation damping trendlines differ between "good" and "bad" quality classes, but no significant difference was found in the (aggregated) internal damping. Differences between the fraction-of-vibrational-energy-radiated FRAD can be estimated straightforwardly for "good-bad" quality classes from the radiation-total damping ratio, sidestepping the intermediate bridge-corpus energy transfer, (i.e., a "bridge-less" violin). Computing FRAD up to 8 kHz reveals: (1) little overall difference between "good" and "bad" violins, and (2) a relative enhancement of radiation in the 3 kHz region for "good" violins due to a shift in effective critical frequency, boosted even further by holding/bowing the violin.