A linear relation between loudness and decibels

A total of 37 uninitiated observers made repeated numerical magnitude judgments of the loudness of a sequence of octave band noises spaced at 1-dB intervals, from 0 to 5 dB above a standard of about 80 dB(A), which was called 10. The observers were not instructed to use numbers as ratios. When the median responses are plotted linearly against decibels, they are fitted by straight lines. Each extra decibel adds an average of 1 unit of loudness, range for individual observers 10 through .25 units. This is consistent with the view that the subjectively equal stimulus spacing for the loudness of noise is linear in decibels, and that the observers use numbers linearly in judging the loudness.