The sound levels of power, intensity and pressure are the physical effects which the human ear receives, it is not, however, what the person perceives. What is being perceived or heard depend on how the human brain interprets or perceives the sound levels received by the ear.
Loudness is the brains' perception of the magnitude of the sound levels. The brain's interpretation of loudness depends on the magnitude of vibration produced in the ear mechanism. The higher levels of sound produce more vibration in the ear mechanism, and vice-versa; and hence, accordingly the brain perceives the sound as loud and not loud respectively.
Thus, what is actually heard is not the decibel (dB) level but the interpretation of it. Therefore, other units are used for loudness which are- phone and some. A phone is the loudness of a tone that is numerically equal to the corresponding sound pressure level when heard at 1000 Hz. Thus, a sound pressure level at 50 dB is 50 phones when heard at 1000 Hz. Fig. 3.13 shows a set of equal loudness contours (phone) that have been internationally standardized. It can be observed from the fig. 3.13 that a given loudness (phone) may have different decibel (dB) level when heard at different frequencies.
The phone scale for the equal loudness level contours is not applicable as a true loudness scale. In other words, the phone unit is not additive. For example, 80 phones don't appear to be twice as loud as 40 phones (i.e., 40 phones to + 40 phones # 80 phones). Fletcher, an early researcher in psychoacoustics, devised a unit of measurement such that the loudness of two or more sources can simply be added. This new unit, sone, is defined as a loudness of a 1000 Hz of 40 dB intensity. The relationship between the loudness level in phones (p) and the subjective level in sones (s) is mathematically expressed as-
S =2(P-40/10)
From the above formula, S=1 sone , when P =40 phones; and S = 2 sones, when P = 50 phones. Therefore, 40 phones + 40 phones = 50 phones (not 80 phones); because in term of sones, I sone + I sone = 2 sones and the process is additive. The results show that the subjective loudness (sones) doubles for an increase of 10 phones. The graphical representation of the above relationship is shown in fig. 3.14.