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{{Short description|Unit of perceived loudness}}
The '''sone''' is a ] of ] ] after a proposal of ] in 1936. In ], loudness is a ] measure of the ]. One sone is equivalent to 40 ]s, which is defined as the loudness of a 1 ] tone at 40 ] ]. The number of sones to a phon was chosen so that a doubling of the number of sones sounds to the ] like a doubling of the ], which also corresponds to increasing the ] by 10 dB, or increasing the sound ] by a factor 3.16 (=<math>\sqrt{10}</math>). At frequencies other than 1 kHz, the measurement in sones must be calibrated according to the frequency response of human ], which is of course a subjective process. The study of apparent loudness is included in the topic of ].
{{other uses}}
{{redirect|Sones}}


The '''sone''' ({{IPAc-en|ˈ|s|oʊ|n}}) is a ] of ], the ] perception of ]. The study of perceived loudness is included in the topic of ] and employs methods of ]. Doubling the perceived loudness doubles the sone value. Proposed by ] in 1936, it is not an ].
To be fully precise, a measurement in sones must be qualified by the optional suffix G, which means that the loudness value is calculated from frequency groups, and by one of the two suffixes F (for free field) or D (for diffuse field).


==Definition and conversions==
== See also ==
According to Stevens' definition, a loudness of 1&nbsp;sone is equivalent to 40&nbsp;]s (a 1&nbsp;] tone at 40&nbsp;]).<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> The phons scale aligns with dB, not with loudness, so the sone and phon scales are not proportional. Rather, the loudness in sones is, at least very nearly, a ] 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 = https://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 = https://books.google.com/books?id=vtubxNaSAdAC&pg=PA613 }}</ref> With this exponent, each 10 phon increase (or 10&nbsp;dB at 1&nbsp;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 = https://books.google.com/books?id=U8cxxaVVjqYC&pg=PA299}}</ref>


:{| class="wikitable" style="text-align:right"
]
|-
]
! ''sone''
]
| 1 || 2 || 4 || 8 || 16 || 32 || 64
]
|-
! ''phon''
| 40 || 50 || 60 || 70 || 80 || 90 || 100
|}


At frequencies other than 1&nbsp;kHz, the loudness level in phons is calibrated according to the frequency response of human ], via a set of ]s, and then the loudness level in phons is mapped to loudness in sones via the same power law.
]

]
Loudness ''N'' in sones (for ''L<sub>N</sub>'' > 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 = https://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''<sub>N</sub> 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 ]s or narrowband signals. For multi-component or broadband signals, a more elaborate loudness model is required, accounting for ]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).

==Example values==
{{Unreferenced section|date=January 2022}}
:{| class="wikitable"
! Description !! Sound pressure !! Sound pressure level !! Loudness
|-
! &nbsp; !! align="center" | pascal !! align="center" | dB re 20&nbsp;μPa !! align="center" | sone
|-
|] || align="right" | ~ 100 || align="right" | ~ 134 ||align="right" | '''~ 676'''
|-
|] during short-term effect || align="right" | ~ 20 || align="right" | ~ 120 || align="right" | '''~ 256'''
|-
|], 100&nbsp;m away || align="right" | 6 ... 200 || align="right" | 110 ... 140 || align="right" | '''128 ... 1024'''
|-
|], 1&nbsp;m away / ] || align="right" | ~ 2 || align="right" | ~ 100 || align="right" | '''~ 64'''
|-
|] || align="right" | ~ 6×10<sup>−1</sup> || align="right" | ~ 90 || align="right" | '''~ 32'''
|-
|Major road, 10&nbsp;m away || align="right" | 2×10<sup>−1</sup> ... 6×10<sup>−1</sup> || align="right" | 80 ... 90 || align="right" | '''16 ... 32'''
|-
|], 10&nbsp;m away || align="right" | 2×10<sup>−2</sup> ... 2×10<sup>−1</sup> || align="right" | 60 ... 80 || align="right" | '''4 ... 16'''
|-
|TV set at home level, 1&nbsp;m away || align="right" | ~ 2×10<sup>−2</sup> || align="right" | ~ 60 || align="right" | '''~ 4'''
|-
|Normal talking, 1&nbsp;m away || align="right" | 2×10<sup>−3</sup> ... 2×10<sup>−2</sup> || align="right" | 40 ... 60 || align="right" | '''1 ... 4'''
|-
|Very calm room || align="right" | 2×10<sup>−4</sup> ... 6×10<sup>−4</sup> || align="right" | 20 ... 30 || align="right" | '''0.15 ... 0.4'''
|-
|Rustling leaves, calm breathing || align="right" | ~ 6×10<sup>−5</sup> || align="right" | ~ 10 ||align="right" | '''~ 0.02'''
|-
|] at 1&nbsp;kHz || align="right" | 2×10<sup>−5</sup> || align="right" | 0 ||align="right" | '''0'''
|}

==See also==
*]
*]
*]
*]

==References==
{{reflist}}

==External links==
*

]
]
]

Latest revision as of 19:03, 20 April 2024

Unit of perceived loudness For other uses, see Sone (disambiguation). "Sones" redirects here. For other uses, see Sones (disambiguation).

The sone (/ˈsoʊn/) is a unit of loudness, the subjective perception of sound pressure. The study of perceived loudness is included in the topic of psychoacoustics and employs methods of psychophysics. Doubling the perceived loudness doubles the sone value. Proposed by Stanley Smith Stevens in 1936, it is not an SI unit.

Definition and conversions

According to Stevens' definition, a loudness of 1 sone is equivalent to 40 phons (a 1 kHz tone at 40 dB SPL). The phons scale aligns with 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.

sone 1 2 4 8 16 32 64
phon 40 50 60 70 80 90 100

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 LN > 40 phon):

N = ( 10 L N − 40 10 ) 0.30103 ≈ 2 L N − 40 10 {\displaystyle 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 ) {\displaystyle 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).

Example values

This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2022) (Learn how and when to remove this message)
Description 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 ~ 120 ~ 256
Jet, 100 m away 6 ... 200 110 ... 140 128 ... 1024
Jackhammer, 1 m away / nightclub ~ 2 ~ 100 ~ 64
Hearing damage during long-term effect ~ 6×10 ~ 90 ~ 32
Major road, 10 m away 2×10 ... 6×10 80 ... 90 16 ... 32
Passenger car, 10 m away 2×10 ... 2×10 60 ... 80 4 ... 16
TV set at home level, 1 m away ~ 2×10 ~ 60 ~ 4
Normal talking, 1 m away 2×10 ... 2×10 40 ... 60 1 ... 4
Very calm room 2×10 ... 6×10 20 ... 30 0.15 ... 0.4
Rustling leaves, calm breathing ~ 6×10 ~ 10 ~ 0.02
Auditory threshold at 1 kHz 2×10 0 0

See also

References

  1. 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
  2. Brian C. J. Moore (2007). Cochlear hearing loss: physiological, psychological and technical issues (2nd ed.). Wiley-Interscience. pp. 94–95. ISBN 978-0-470-51633-1.
  3. Irving P. Herman (2007). Physics of The Human Body. Springer. p. 613. ISBN 978-3-540-29603-4.
  4. Eberhard Hänsler, Gerhard Schmidt (2008). Speech and audio processing in adverse environments. Springer. p. 299. ISBN 978-3-540-70601-4.
  5. Hugo Fastl and Eberhard Zwicker (2007). Psychoacoustics: facts and models (3rd ed.). Springer. p. 207. ISBN 978-3-540-23159-2.

External links

Categories: