An alternative mathematical description of the relationship between noise exposure and hearing loss

Retrospective investigation of large populations has provided means for determining quantitative relationships between the hearing levels of non-noise-exposed populations and age, and between the hearing levels of noise-exposed populations and age and noise exposure. In the latter case, noise exposures have been predominantly steady state over many years and no way of measuring the effects of noise alone, excluding the effects of age, has ever been demonstrated. In the following paper, attention is confined to the problem of developing a mathematical description of an existing set of empirically determined hearing level data; questions of audiology are not of concern here. It is shown that the mathematical analysis traditionally used to determine the contribution of noise exposure alone to hearing level is not unique; an alternative formulation is possible and indeed is demonstrated. Whereas the traditional formulation leads to the conclusion that noise-induced hearing loss scales on the integral of sound pressure squared with time, and thus, to the equal energy hypothesis, the alternative formulation leads to the conclusion that noise-induced hearing loss scales on the integral of pressure with time. Since either formulation adequately describes the data, and the equal energy hypothesis has never been adequately substantiated, use of the latter hypothesis to extend the findings of steady-state exposures to application for unsteady exposures is not justified. The alternative formulation presented here is recommended for consideration.