Sone
Encyclopedia
The sone was proposed as a unit of perceived
loudness
by Stanley Smith Stevens
in 1936. In acoustics
, loudness is the subjective
perception of sound intensity. Although defined by Stevens as a unit, it is not one of the SI
units.
According to Stevens' definition, a loudness of 1 sone is equivalent to the loudness of a signal at 40 phon
s, 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 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.
or loudness level LN in phons (for N > 1 sone):
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 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).
Perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...
loudness
Loudness
Loudness is the quality of a sound that is primarily a psychological correlate of physical strength . More formally, it is defined as "that attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud."Loudness, a subjective measure, is often...
by Stanley Smith Stevens
Stevens' power law
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...
in 1936. In acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
, loudness is the subjective
Subjectivity
Subjectivity refers to the subject and his or her perspective, feelings, beliefs, and desires. In philosophy, the term is usually contrasted with objectivity.-Qualia:...
perception of sound intensity. Although defined by Stevens as a unit, it is not one of the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units.
According to Stevens' definition, a loudness of 1 sone is equivalent to the loudness of a signal at 40 phon
Phon
The phon was proposed in DIN 45631 and ISO 532 B as a unit of perceived loudness level LN for pure tones by S. S. Stevens.-Definition:The purpose of the phon scale is to compensate for the effect of frequency on the perceived loudness of tones...
s, the loudness level of a 1 kHz tone at 40 dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
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
Hearing (sense)
Hearing is the ability to perceive sound by detecting vibrations through an organ such as the ear. It is one of the traditional five senses...
, via a set of equal-loudness contour
Equal-loudness contour
An equal-loudness contour is a measure of sound pressure , over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours...
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
Psychoacoustics
Psychoacoustics is the scientific study of sound perception. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound...
and employs methods of psychophysics.
Formulas
Loudness N in sones (for LN > 40 phon):
or loudness level LN in phons (for N > 1 sone):
Corrections are needed at lower levels, near the threshold of hearing.
These formulas are for single-frequency sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...
s 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 sound | sound pressure | sound pressure level | loudness |
|---|---|---|---|
| | pascal | | dB re 20 µPa | | sone | |
| threshold of pain Threshold of pain The threshold of pain is the point at which pain begins to be felt. It is an entirely subjective phenomenon. The intensity at which a stimulus begins to evoke pain is the threshold intensity. So, if a hotplate on a person's skin begins to hurt at 42°C , then that is the pain threshold temperature... |
100 | 134 | ~ 676 |
| hearing damage during short-term effect | 20 | approx. 120 | ~ 256 |
| jet Jet engine A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets... , 100 m away |
6 ... 200 | 110 ... 140 | ~ 128 ... 1024 |
| jack hammer, 1 m away / discotheque | 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 Automobile An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor... , 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 |
See also
- Sound pressure level
- PhonPhonThe phon was proposed in DIN 45631 and ISO 532 B as a unit of perceived loudness level LN for pure tones by S. S. Stevens.-Definition:The purpose of the phon scale is to compensate for the effect of frequency on the perceived loudness of tones...
- dB(A)
- Stevens' power lawStevens' power lawStevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...
- Weber–Fechner lawWeber–Fechner lawThe Weber–Fechner law is a confusing term, because it combines two different laws. Some authors use the term to mean Weber's law, and others Fechner's law. Fechner himself added confusion to the literature by calling his own law Weber's law...