Sone

"Sones" redirects here. For other uses, see Sones (disambiguation).

The sone is a unit of how loud a sound is perceived. The sone scale is linear. Doubling the perceived loudness doubles the sone value. Proposed by Stanley Smith Stevens in 1936, it is a non-SI unit.

In acoustics, loudness is the subjective perception of sound pressure. The study of apparent loudness is included in the topic of psychoacoustics and employs methods of psychophysics.

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

Source of sound	sound pressure	sound pressure level	loudness
	pascal	dB re 20 µPa	sone
threshold of pain	100	134	~ 676
hearing damage during short-term effect	20	approx. 120	~ 256
jet, 100 m away	6 ... 200	110 ... 140	~ 128 ... 1024
jack hammer, 1 m away / nightclub	2	approx. 100	~ 64
hearing damage during long-term effect	6×10−1	approx. 90	~ 32
major road, 10 m away	2×10−1 ... 6×10−1	80 ... 90	~ 16 ... 32
passenger car, 10 m away	2×10−2 ... 2×10−1	60 ... 80	~ 4 ... 16
TV set at home level, 1 m away	2×10−2	ca. 60	~ 4
normal talking, 1 m away	2×10−3 ... 2×10−2	40 ... 60	~ 1 ... 4
very calm room	2×10−4 ... 6×10−4	20 ... 30	~ 0.15 ... 0.4
leaves' noise, calm breathing	6×10−5	10	~ 0.02
auditory threshold at 1 kHz	2×10−5	0	0

sone	1	2	4	8	16	32	64	128	256	512	1024
phon	40	50	60	70	80	90	100	110	120	130	140

Formulae

According to Stevens' definition, 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. With this exponent, each 10 phon increase (or 10 dB at 1 kHz) produces almost exactly a doubling of the loudness in sones.

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.

Loudness N in sones (for L_N > 40 phon):

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

or loudness level L_N 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).

See also

• Sound pressure level
• Phon
• dB(A)
• Decibel
• Stevens' power law
• Weber–Fechner law

External links

• Conversion: Loudness N (sones) to loudness level L (phons) and loudness level L (phons) to loudness N (sones)