proposé

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Note added at 6 hrs (2015-02-11 00:43:55 GMT)
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(Tmax_Tmin)/2 au carré

Another formulation

In all scientific fields, dealing with waves, uses the root-mean-square (r.m.s.) formula to determine the average (effective) value (moyenne quadratique, valeur efficace). This is also valid for acoustics.

The averaged (r.m.s.) sound pressure value is compared to the reference level (10 exp(-12) W/m*m). The logarithm of this ratio is then multiplied by 10. Example: If the sound pressure ratio results in 8 Bel, it will be expressed as 80 decibel, the loudness of a noisy street.

Note: These explanations have been verified by consulting my reference books for physics.

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Note added at 16 hrs (2015-02-11 10:52:25 GMT)
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Sound intensity
In a sound wave, the complementary variable to sound pressure is the particle velocity. Together they determine the sound intensity of the wave.
Sound intensity, denoted I and measured in W•m−2, is given by:
I = pv
where:
• p is the sound pressure, measured in Pa;
• v is the particle velocity, measured in m•s−1.
:
Sound pressure level (SPL) or acoustic pressure level is a logarithmic measure of the effective sound pressure of a sound relative to a reference value.
Sound pressure level, denoted Lp and measured in dB, above a standard reference level, is given by:
Lp = 10 log 10 (p rms²/p 0²) = 20 log10 (p rms/p 0) dB (SPL)
where:
• prms is the root mean square sound pressure, measured in Pa;[3]
• p0 is the reference sound pressure, measured in Pa.
The commonly used reference sound pressure in air is p0 = 20 μPa (RMS) or 0.0002 dynes/cm2, which is usually considered the threshold of human hearing (roughly the sound of a mosquito flying 3 m away).
http://en.wikipedia.org/wiki/Sound_pressure#Sound_pressure_l...

La pression acoustique est la valeur efficace, sur un intervalle de temps donné, de l'amplitude de la variation rapide de la pression atmosphérique qui cause une impression sonore. L'unité SI pour la pression est le pascal (équivalent au N/m², symbole : Pa) ; cette unité s'applique à la pression acoustique.
:
Pression acoustique efficace (RMS)
Pour les mesures de niveau sonore, on s'intéresse moins aux valeurs de la pression sonore instantanée qu'à la puissance que les ondes sonores peuvent mobiliser, dont dépendent les effets du son, notamment sur l'oreille. C'est donc cette puissance, proportionnelle au carré de la pression acoustique, qui sert pour évaluer le niveau sonore.
http://fr.wikipedia.org/wiki/Pression_acoustique


● Decibel Table − SPL − Loudness Comparison Chart ●

Table of Sound Levels (dB Scale) and the corresponding Units of Sound Pressure and Sound Intensity (Examples)
Decibel level and comparison of common sounds
:
The values are averaged and can differ about ±10 dB. With sound pressure p is
always meant the root mean square value (RMS) of the sound pressure, without
extra announcement. The amplitude of the sound pressure means the peak value.
The sound pressure (RMS) is the most important quantity in sound measurement.
Example from the table below:
Kerbside of busy road, 5 m 80 dB;
Sound pressure 0.2 N/m² (Pa)
Sound intensity 0.0001 W/m²
http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm

Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level. Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors.
Lp = 20 log10 (p/p 0) = 10 log10 (p/p 0)²

The usual reference level po is 20x10-6 N/m2. Note that the noise from motors is documented in sound power level. "Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than 10-9 of atmospheric pressure or about 20x10-5 N/m2 at 1000 Hz. "Threshold of pain'' corresponds to a pressure 106 times greater, but still less than 1/1000 of atmospheric pressure. Because of the wide range, sound pressure measurements are made on a logarithmic scale (decibel scale).
http://www.usmotors.com/TechDocs/ProFacts/Sound-Power-Pressu...

inverse square law Sound Pressure Level. Sound propagates in all directions to form a spherical field, thus sound energy is inversely proportional to the square of the distance, i.e., doubling the distance quarters the sound energy (the inverse square law), so SPL is attenuated 6 dB for each doubling.
:
sound pressure level or SPL 1. A measure of intensity. The rms sound pressure expressed in dB re 20 microPa (the lowest threshold of hearing for 1 kHz). [As points of reference, 0 dB-SPL equals the threshold of hearing, while 140 dB-SPL equals irreparable hearing damage.] See: inverse square law
http://www.rane.com/par-s.html#SPL

In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids.
:
The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the original values (or the square of the function that defines the continuous waveform).
http://en.wikipedia.org/wiki/Root_mean_square

La moyenne quadratique est une moyenne d'une liste de valeurs, définie comme la racine de la moyenne des carrés des valeurs :
http://fr.wikipedia.org/wiki/Moyenne_quadratique

Conclusion : La moyenne quadratique est implique automatiquement dans le calcul de la pression acoustique, même si elle n’est pas mentionnée expressivement.

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Note added at 1 day16 hrs (2015-02-12 10:42:43 GMT)
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As some peers may not be familiar with the laws of logarithms, I think it is useful to copy also the relevant explanations from Wikipedia and other sources:

In mathematics, the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 10 to the power 3 is 1000: 1000 = 10 × 10 × 10 = 103. … The logarithm to base 10 (b = 10) is called the common logarithm and has many applications in science and engineering
:
The logarithm of the p-th power of a number is p times the logarithm of the number itself; the logarithm of a p-th root is the logarithm of the number divided by p.
http://en.wikipedia.org/wiki/Logarithm

Le logarithme de base b d'un nombre réel strictement positif est la puissance à laquelle il faut élever la base b pour obtenir ce nombre. Par exemple, le logarithme de mille en base dix est 3, car 1000 = 103. Le logarithme de x en base b est noté logb(x). Ainsi log10(1000) = 3.
http://fr.wikipedia.org/wiki/Logarithme

En acoustique, une différence de un décibel ou un dB entre deux puissances signifie que le logarithme du rapport entre ces deux puissances est de 0,1 (un dixième de bel). Sachant qu'un logarithme de 0,1 correspond à un nombre égal à 1,26, une augmentation de 1 dB correspond à une multiplication de la puissance par 1,26. Une multiplication de la puissance sonore par 2 correspond à une augmentation de 3 dB.
http://fr.wikipedia.org/wiki/Logarithme_décimal

See also the laws of logarithms :

Third Law (for exponentiation of number)
Log An = n log A
http://www.mathcentre.ac.uk/resources/uploaded/mc-bus-loglaw...

Loi du logarithme
3- = Loi du logarithme d’une puissance
Log a MN = NLog a M
http://www.cableamos.com/sylvain.lacroix/maths/526-536/log/l...

e.g. log a² = 2 log a or in our application: 10 log a² = 20 log a.

The logarithmic notation reduces the exponentiation to a simple multiplication and eliminates all "carrés"