The subjectively perceived strength of a sound. There is a complex relationship between this psychophysical quantity and objectively measured attributes of the sound wave. The loudness of a sound is most directly related to the intensity, which is the energy transmitted by the sound wave across unit area per second; it is also influenced by the duration and the frequency spectrum of the sound, and by the context in which the sound is heard.
It has often been suggested that subjective loudness is proportional to the logarithm of the sound intensity (an example of the Weber-Fechner psychophysical law, which states that sensation is proportional to the logarithm of stimulus). The intensity level is a logarithmic intensity measure: if the intensity is multiplied by n powers of ten, then the intensity level increases by n bels or 10n decibels (dB). For example, if one sound has twice the intensity of another, the difference in intensity is 3 dB, if the first sound is ten times more intense the difference is 10 dB, and if the first sound is a million times more intense the difference is 60 dB. The reference intensity corresponding to 0 dB is chosen to be one picowatt per square metre, which is below the threshold of audibility for almost all human listeners. The loudness level, whose unit is the phon, also takes account of the fact that the ear’s response varies with frequency; the phon rating of a sound is numerically equal to the intensity level (in dB) of an equally loud sinusoidal tone at the standard frequency of 1000 Hz.
A rough correspondence can be established between loudness level and the musical dynamic scale, with a change of 10 phons being approximately equivalent to one dynamic step (for example, from mezzo-forte to forte). Loudness level is not, however, directly proportional to loudness. A fortissimo sound might be rated at 90 phons, and a pianissimo sound at 45 phons: most listeners would judge the loudness ratio of these sounds to be much greater than two. Psychoacoustic studies of loudness ratio estimation have established that a doubling of loudness corresponds roughly to an increase of 10 phons. This is the basis of the sone loudness scale: 1 sone is equivalent to 40 phons, 2 sones to 50 phons, 4 sones to 60 phons and so on. The empirically verified sone scale implies that subjective loudness is not proportional to the logarithm of the sound intensity, but rather to the cube root of the intensity.
See also Sound.
L.E. Kinsler and others: Fundamentals of Acoustics (New York, 3/1982)
M. Campbell and C. Greated: The Musician’s Guide to Acoustics (London, 1987/R)
J.G. Roederer: The Physics and Psychophysics of Music (New York, 3/1995)
MURRAY CAMPBELL, CLIVE GREATED