The fact that Weber's law appears to apply in the same way both to intensity discrimination for pure tones and to intensity discrimination for white noise poses a theoretical paradox: in the case of pure tones, the human observer becomes less efficient as the intensity of the tone is increased, while in the case of white noise he exhibits a constant efficiency independent of intensity.
An inventory of the various possible noise sources which may exist is made, and the way in which these may be expected to effect the detectability of a signal leads to the equation
, where η is the individual observer′s efficiency, NG
is the noise introduced by the experimenter, NE
is the uncontrolled noise present in the experimental situation, and k
is a constant indicating that small amplitude variation in the oscillator constitutes a noise source proportional to the power of the lower of two signals to be discriminated.
Data for three observers over four noise levels is described by this equation sufficiently well to suggest that the hypothesis that Weber's law is merely a reflection of the oscillator noise (kV02) is plausible.