Structural acoustics of good and bad violins

Modal-acoustic radiation measurements on 17 "bad-to-excellent" quality-rated violins--including three-dimensional modal analyses of Titian and Willemotte Stradivari and Plowden Guarneri del Gesu violins to investigate extensional as well as flexural motions-were examined for quality-related trends, generally by contrasting the properties of "excellent" and "bad" violins. All violins tested showed the same five "signature" modes below 600 Hz, with no obvious quality trends for mode frequencies or total damping. Bad-excellent comparisons of band-/modal-averaged damping (total, radiation and internal), mobility, radiativity, directivity, fraction-of-vibrational-energy radiated, effective critical frequency, and radiativity profiles up to 4 kHz generally showed no significant difference; the only "robust" quality differentiator was the approximately 280 Hz, Helmholtz-type A0 cavity mode radiativity where excellent violins were significantly higher. Radiation and total damping of two old Italian violins appeared slightly higher than those for bad violins below 2 kHz, partly due to lower effective critical frequency and partly because of slightly lower mass. Stradivari violins showed the highest and lowest directivity of all instruments tested. The Titian and Plowden top plate flexural/extensional mobility ratios appeared correlated with their directivity. Extensional motion in the "bridge island" between f holes peaked near 2.4 kHz, coinciding with the BH peak and a bridge/bridge-island impedance ratio minimum.