Mathematical model of the effect of limited stapes displacement on hazard from intense sounds

Abstract

As a follow-on to an idea presented earlier [G. R. Price, J. Acoust. Soc. Am. 56, 195–197 (1974)] an integrated mathematical model of the external, middle, and inner ears has been developed for the cat ear. It allows the calculation of stapes displacements (among other values) in response to any free-field sound pressure. An absolute limit to displacement of about 20 μ peak to peak is assumed, based on the dimensions of the annular ligament and in accord with the measurements of Guinan and Peake [J. Acoust Soc. Am. 41, 1237–1261 (1967)]. Where hazard from intense impulses, such as gunfire, are concerned, the effect of this limitation on stapes displacement is profound, producing a spectral bias (higher velocities being transmitted at high frequencies) as well as the blocking of transmission into the cochlea when amplitudes exceed the limiting values. This action may in part explain why low-frequency impulses are much less hazardous than their energy content would seem to indicate as well as why hearing losses are not more severe for very intense sounds (150 dB and up) commonly found around weapons.