The sone () is a unit of loudness, the

subjective Subjective may refer to: * Subjectivity, a subject's personal perspective, feelings, beliefs, desires or discovery, as opposed to those made from an independent, objective, point of view ** Subjective experience, the subjective quality of conscio ...

perception of

sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone ...

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

psychophysics Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they produce. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, m ...

. Doubling the perceived loudness doubles the sone value. Proposed by

Stanley Smith Stevens Stanley Smith Stevens (November 4, 1906 – January 18, 1973) was an American psychologist who founded Harvard's Psycho-Acoustic Laboratory, studying psychoacoustics, and he is credited with the introduction of Stevens's power law. Stevens author ...

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 The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...

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 In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...

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 An equal-loudness contour is a measure of sound pressure level, 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 ...

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_N'' > 40 phon): :

N = \left(10^\right)^ \approx 2^

or loudness level ''L''_N in phons (for ''N'' > 1 sone): :

L_N = 40 + 10 \log_(N)

Corrections are needed at lower levels, near the threshold of hearing. These formulas are for single-frequency

sine wave A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...

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).

Example values

References

{{reflist

External links

Correlation between sones und phons − calculator
Hearing Human-based units of measurement Units of sound

Definition and conversions

Example values

See also

References

External links