# Sone

The sone is a unit of perceived loudness proposed by Stanley Smith Stevens in 1936. In acoustics, loudness is the subjective perception of sound pressure. It is a non-SI unit.

According to Stevens' definition,[1] a loudness of 1 sone is equivalent to the loudness of a signal at 40 phons, the loudness level of a 1 kHz tone at 40 dB SPL. But phons scale with level in dB, not with loudness, so the sone and phon scales are not proportional. Rather, the loudness in sones is, at least very nearly, a power law function of the signal intensity, with an exponent of 0.3.[2][3] With this exponent, each 10 phon increase (or 10 dB at 1 kHz) produces almost exactly a doubling of the loudness in sones.[4]

At frequencies other than 1 kHz, the loudness level in phons is calibrated according to the frequency response of human hearing, via a set of equal-loudness contours, and then the loudness level in phons is mapped to loudness in sones via the same power law.

The study of apparent loudness is included in the topic of psychoacoustics and employs methods of psychophysics.

## Formulas

Loudness N in sones (for LN > 40 phon):[5]

$N = \left(10^{\frac{L_N-40}{10}}\right)^{0.30103} \approx 2^{\frac{L_N-40}{10}}$

or loudness level LN in phons (for N > 1 sone):

$L_N = 40 + 10 \log_{2}(N)$

Corrections are needed at lower levels, near the threshold of hearing.

These formulas are for single-frequency sine waves or narrowband signals. For multi-component or broadband signals, a more elaborate loudness model is required, accounting for critical bands.

To be fully precise, a measurement in sones must be specified in terms of the optional suffix G, which means that the loudness value is calculated from frequency groups, and by one of the two suffixes D (for direct field or free field) or R (for room field or diffuse field).

## Examples of sound pressure, sound pressure levels, and loudness in sone

Source of soundsound pressuresound pressure levelloudness
pascaldB re 20 µPasone
threshold of pain100134~ 676
hearing damage during short-term effect20approx. 120~ 256
jet, 100 m away6 ... 200110 ... 140~ 128 ... 1024
jack hammer, 1 m away / discotheque2approx. 100~ 64
hearing damage during long-term effect6×10−1approx. 90~ 32
major road, 10 m away2×10−1 ... 6×10−180 ... 90~ 16 ... 32
passenger car, 10 m away2×10−2 ... 2×10−160 ... 80~ 4 ... 16
TV set at home level, 1 m away2×10−2ca. 60~ 4
normal talking, 1 m away2×10−3 ... 2×10−240 ... 60~ 1 ... 4
very calm room2×10−4 ... 6×10−420 ... 30~ 0.15 ... 0.4
leaves' noise, calm breathing6×10−510~ 0.02
auditory threshold at 1 kHz2×10−500
 sone phon 1 2 4 8 16 32 64 128 256 512 1024 40 50 60 70 80 90 100 110 120 130 140