The Fechner-Weber law states that for a sensation’s intensity to increase in an arithmetic progression, the stimulus must increase in a geometric progression. This relation describes sensory perceptions and physical stimuli for hearing. Human hearing can detect noise so quiet that the eardrum moves less than an atom’s width, and noise 10 trillion times more powerful. Similarly, the faintest star we can see is about 10 trillion times less powerful than the Sun. In a noisy environment, we can distinguish quieter sounds, such as conversation or a dropped coin. Senses respond not to the absolute increase in a stimulus, but to fractional increase. Ernst Heinrich Weber showed in 1846 that the change in a person’s perception of weight was proportional to the logarithm of any increase. For acoustics, as a stimulus becomes ten times stronger, the perceived increase only doubles. Gustav Fechner elaborated on Weber’s discovery in 1860. The Fechner-Weber law can be experienced by halfing noise. If our sense of hearing was linear with respect to intensity, that would reduce the noise by half. However, although the sound power in the room has halved, the difference in the volume we hear is barely noticeable.
References:
Weber, E.H., 1851. Annotationes anatomicae et physiologicae: Tractatus de motu iridis summa doctrinae de motu iridis. Koehler.
Fechner, G. T. (1860). Elemente der Psychophysik.