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2014-01-29T02:19:45Z

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{{redirect|Sones}}
The '''sone''' is a [[physical unit|unit]] of [[perception|perceived]] [[loudness]] proposed by [[Stevens' power law|Stanley Smith Stevens]] in 1936. In [[acoustics]], loudness is the [[Subjectivity|subjective]] perception of [[sound pressure]]. It is a non-[[SI]] unit.

According to Stevens' definition,<ref>Stanley Smith Stevens: A scale for the measurement of the psychological magnitude: loudness. See: Psychological Review. 43, Nr. 5,APA Journals, 1936, pp. 405-416</ref> a loudness of 1 sone is equivalent to the loudness of a signal at 40 [[phon]]s, the ''loudness level'' of a 1 [[kilohertz|kHz]] tone at 40 [[decibel|dB]] [[sound pressure level|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.<ref>{{cite book
| title = Cochlear hearing loss: physiological, psychological and technical issues | edition = 2nd | author = Brian C. J. Moore | publisher = Wiley-Interscience | year = 2007 | isbn = 978-0-470-51633-1 | pages = 94–95 | url = http://books.google.com/books?id=G6SbxrLVWn4C&pg=PA94 }}</ref><ref>{{cite book | title = Physics of The Human Body | author = Irving P. Herman | publisher = Springer | year = 2007 | isbn = 978-3-540-29603-4 | page = 613 | url = http://books.google.com/books?id=vtubxNaSAdAC&pg=PA613 }}</ref> With this exponent, each 10 phon increase (or 10 dB at 1 kHz) produces almost exactly a doubling of the loudness in sones.<ref>{{cite book | title = Speech and audio processing in adverse environments | author = Eberhard Hänsler, Gerhard Schmidt | publisher = Springer | year = 2008 | isbn = 978-3-540-70601-4 | page = 299 | url = http://books.google.com/books?id=U8cxxaVVjqYC&pg=PA299}}</ref>

At frequencies other than 1 kHz, the loudness level in phons is calibrated according to the frequency response of human [[hearing (sense)|hearing]], via a set of [[equal-loudness contour]]s, 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):<ref>
{{cite book
| title = Psychoacoustics: facts and models
| edition = 3rd
| author = Hugo Fastl and Eberhard Zwicker
| publisher = Springer
| year = 2007
| isbn = 978-3-540-23159-2
| page = 207
| url = http://books.google.com/books?id=eGcfn9ddRhcC&pg=PA207
}}</ref>
:<math>
N = \left(10^{\frac{L_N-40}{10}}\right)^{0.30103} \approx 2^{\frac{L_N-40}{10}}
</math>

or loudness level ''L''N in phons (for ''N'' > 1 sone):
:<math>
L_N = 40 + 10 \log_{2}(N)
</math>

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

These formulas are for single-frequency [[sine wave]]s or narrowband signals. For multi-component or broadband signals, a more elaborate loudness model is required, accounting for [[critical band]]s.

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==

:{| class="wikitable"
! Source of sound !! sound pressure !! sound pressure level !! loudness
|-
!   !! align="center" | pascal !! align="center" | dB re 20 µPa !! align="center" | sone
|-
|[[threshold of pain]] || align="right" | 100 || align="right" | 134 ||align="right" | '''~ 676'''
|-
|[[Noise-induced hearing loss|hearing damage]] during short-term effect || align="right" | 20 || align="right" | approx. 120 || align="right" | '''~ 256'''
|-
|[[Jet engine|jet]], 100 m away || align="right" | 6 ... 200 || align="right" | 110 ... 140 || align="right" | '''~ 128 ... 1024'''
|-
|[[jack hammer]], 1 m away / [[discotheque]] || align="right" | 2 || align="right" | approx. 100 || align="right" | '''~ 64'''
|-
|[[Noise-induced hearing loss#Gradually developing NIHL|hearing damage during long-term effect]] || align="right" | 6×10−1 || align="right" | approx. 90 || align="right" | '''~ 32'''
|-
|major road, 10 m away || align="right" | 2×10−1 ... 6×10−1 || align="right" | 80 ... 90 || align="right" | '''~ 16 ... 32'''
|-
|[[automobile|passenger car]], 10 m away || align="right" | 2×10−2 ... 2×10−1 || align="right" | 60 ... 80 || align="right" | '''~ 4 ... 16'''
|-
|TV set at home level, 1 m away || align="right" | 2×10−2 || align="right" | ca. 60 || align="right" | '''~ 4'''
|-
|normal talking, 1 m away || align="right" | 2×10−3 ... 2×10−2 || align="right" | 40 ... 60 || align="right" | '''~ 1 ... 4'''
|-
|very calm room || align="right" | 2×10−4 ... 6×10−4 || align="right" | 20 ... 30 || align="right" | '''~ 0.15 ... 0.4'''
|-
|leaves' noise, calm breathing || align="right" | 6×10−5 || align="right" | 10 ||align="right" | '''~ 0.02'''
|-
|[[auditory threshold]] at 1 kHz || align="right" | 2×10−5 || align="right" | 0 ||align="right" | '''0'''
|}

:{| class="wikitable"
|-
! ''sone''
|   1  ||   2  ||   4  ||   8  ||  16  ||  32  ||  64  || 128 || 256 || 512 || 1024
|-
! ''phon''
| 40 || 50 || 60 || 70 || 80 || 90 || 100 || 110 || 120 || 130 || 140
|}

==See also==

*[[Sound pressure level]]
*[[Phon]]
*[[dB(A)]]
*[[Stevens' power law]]
*[[Weber–Fechner law]]

==References==

{{reflist}}

==External links==
*[http://www.sengpielaudio.com/calculatorSonephon.htm Conversion: Loudness ''N'' (sones) to loudness level ''L'' (phons) and loudness level ''L'' (phons) to loudness ''N'' (sones)]

[[Category:Hearing]]
[[Category:Human-based units of measurement]]
[[Category:Units of sound]]

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