Weber's Law, Power Law, and Internal Noise
E. G. J. Eijkman, JOHAN M. THIJSSEN, A. J. H. Vendrik · The Journal of the Acoustical Society of America · 1966
Psychophysical experiments concerning the differential sensitivity of the ear for a 1000-cps tone are analyzed. The hypothesis that Weber's law is a case of multiplicative noise was tested. Multiplicative noise exists in systems with fluctuating gain. It can be shown that systems with multiplicative noise displaying Weber's law ΔI/I = CONSTANT possess a power function that relates the relevant neural activity and the stimulus magnitude. The experiments deny, however, a fluctuating gain as the only explanation of Weber's law. The experiments are better described by assuming that observers choose their sensitivity in accordance with the range of stimulus intensities. The internal noise, measured as an equivalent ΔI in the experiment, depends on the range to which the observer has tuned in. A multirange-meter model is discussed, which obeys Weber's law and also shows a restricted class of input-output relations.