Limitations of first-order approximations for calculations using intensity jnd's.
The way in which the noninfinitesimal size of the intensity jnd affects calculations using power functions for pure-tone loudness and neural count is examined. The results of the commonly used first-order differential for representing the change in the power functions due to a jnd in intensity are compared with the second-order approximation and the exact formula. Examples are taken from a variety of psychophysical studies dealing with loudness and intensity discrimination. The second-order and exact formulas are shown to be more consistent with experimental data than the first-order differential.
D004056:Differential Threshold / Q000502:physiology; D006801:Humans; D008144:Loudness Perception / Q000502:physiology; D008433:Mathematics; D008959:Models, Neurological; D009622:Noise