LOUDNESS

in acoustics, attribute of sound that determines the intensity of auditory sensation produced. The loudness of sound as perceived by human ears is roughly proportional to the logarithm of sound intensity: when the intensity is very small, the sound is not audible; when it is too great, it becomes painful and dangerous to the ear. The amount of sound energy that the ear can tolerate is nearly 2 1012 times greater than the amount that is just perceptible. This range varies from person to person and with the frequency of the sound. A unit of loudness, called the phon, has been established; one phon is equal to a difference in sound intensity of one decibel. The number of phons of a given sound is equal to the number of decibels (q.v.) of a pure 1,000-hertz tone judged by the listener to be equally loud. The increase in loudness of any sound is said to be one phon when judged equal to the increase of one decibel in intensity for a 1,000-hertz tone. Because loudness does not appear to increase proportionately with the number of phons (e.g., 60 phons does not seem twice as loud as 30 phons), another more practical unit of loudness, the sone, is used. One sone is defined as the loudness of a tone having a loudness level of 40 phons. On this scale, a sound that is perceived as twice as loud as this reference sound would have a loudness of two sones. In equation form, expressing sones as S and phons as P, log10S = 0.03(P - 40), approximately.