Sensory constraints on auditory identification of the material and geometric properties of struck bars

A computational formula is derived for estimating the constraints limited auditory sensitivity imposes on auditory identification of the material and geometric properties of struck bars. The formula combines a model of the transverse motion of the bar with empirical psychometric functions to map out "null" regions in the bar's physical parameter space where changes in the frequency, amplitude, and decay of partials are likely below threshold for detection. Parameters of the physical space include bar density, Young's modulus, fluid and viscoelastic damping factors, bar length, and bar cross-sectional area (as related to bar shape and hollowness). The formula is used to estimate the possible effect of limited sensitivity in past studies on the auditory identification of bar attributes. The results suggest that sensitivity may, indeed, have played a role in some studies, and that apparent discrepancies in results may be understood based on whether the predominant source of damping was internal or external to the bar. The formula identifies conditions representing an expected bound on identification performance and thereby may be used to aid in the design of future studies for which the struck bar is the sound source of choice.