R&D Report 1954-03 : Subjective judgments on brightness.
G.I. Ross
Experiments have been conducted in the field of acoustics in order to determine whether it is possible for people to judge with any accuracy that one sound is twice as loud as another standard sound, or half as loud as the standard sound. It was found that people can be persuaded to make judgements of "twice as loud" and their results appear to be consistent within reasonable limits. It was concluded that one sound needs to be approximately ten times the intensity of another sound (or have ten times the energy) for it to seem twice as loud, to a statistically average listener.

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