Sound exposure is the integral, over time, of squared

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 hydrop ...

. The

SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

of sound exposure is the

pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...

squared second (Pa²·s).

Mathematical definition

Sound exposure, denoted ''E'', is defined by :

E = \int_^ p(t)^2\, \mathrmt,

where *the exposure is being calculated for the time interval between times ''t''₀ and ''t''₁; *''p(t)'' is the

at time ''t'', usually A-weighted for sound in air.

Sound exposure level

Sound exposure level (SEL) is a

logarithmic measure In mathematics, the set of positive real numbers, \R_ = \left\, is the subset of those real numbers that are greater than zero. The non-negative real numbers, \R_ = \left\, also include zero. Although the symbols \R_ and \R^ are ambiguously used ...

of the sound exposure of a sound relative to a reference value.
Sound exposure level, denoted ''L''_''E'' and measured in dB, is defined by"Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units"
''IEC 60027-3 Ed. 3.0'', International Electrotechnical Commission, 19 July 2002. :

L_E = \frac \ln\!\left(\frac\right)\!~\mathrm = \log_\!\left(\frac\right)\!~\mathrm = 10 \log_\!\left(\frac\right)\!~\mathrm,

where *''E'' is the sound exposure; *''E''₀ is the reference sound exposure; * is the

neper The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. A ...

; * is the

bel BEL can be an abbreviation for: * The ISO 3166-1 alpha-3 country code for Belgium * ''BEL'' or bell character in the C0 control code set * Belarusian language, in the ISO 639-2 and SIL country code lists * Bharat Electronics Limited, an Indian sta ...

; * is the

decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...

. The commonly used reference sound exposure in air isRoss Roeser, Michael Valente, ''Audiology: Diagnosis'' (Thieme 2007), p. 240. :

E_0 = 400~\mathrm.

The proper notations for sound exposure level using this reference are or , but the notations , , dBSEL, or dB_SEL are very common, even if they are not accepted by the SI.Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", ''Guide for the Use of the International System of Units (SI) 2008 Edition'', NIST Special Publication 811, 2nd printing (November 2008), SP81
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References

{{Reflist Sound measurements Physical quantities