The loudness level of a sound is expressed in the dimensionless phon scale and can only be measured by a subjective hearing test. The loudness level amounts to "n" phon when it is judged by a normal observer under standardized listening conditions to be as loud as a pure tone of frequency 1,000 Hz consisting of a plane progressive sound wave coming directly in front of the observer, with the sound pressure = "n" decibels.


Loudness levels in the decibel or phon scales do not immediately correspond to the sensation of loudness but must be interpreted by the listener on the basis of her/his personal experience of sounds of known phon value. The sone scale is a means of expressing the subjective sensation of loudness.


loudness in sone =

= 2 ^ ((0.1 * (loudness level in phon)) - 40)


loudness level in phon =

= (10 * (LOG10 (loudness in sone)) / (LOG10(2))) + 40 =

= (33.219 * (LOG10 (loudness in sone))) + 40



• The equation has been confirmed experimentally over the range of 20 - 120 phon. Outside this range the equations should be viewed as an extrapolation.



(1) A loudness of 1 sone corresponds to a loudness level of 40 phon.

(2) A two-fold change in loudness corresponds to a loudness level difference of 10 phon (the sone doubles for each increase in 10 phon).


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