Sound exposure

Sound measurements
Characteristic	Symbols
Sound pressure	p, SPL
Particle velocity	v, SVL
Particle displacement	δ
Sound intensity	I, SIL
Sound power	P, SWL
Sound energy	W
Sound energy density	w
Sound exposure	E, SEL
Acoustic impedance	Z
Speed of sound	c
Audio frequency	AF
Transmission loss	TL

Sound exposure is the integral, over time, of squared sound pressure. The SI unit of sound exposure is the pascal squared second (Pa²·s).

Mathematical definition

Sound exposure, denoted E, is defined by

E=\int _{{t_{0}}}^{{t_{1}}}p(t)^{2}\,{\mathrm {d}}t,

where

the exposure is being calculated for the time interval between times t₀ and t₁;
p(t) is the sound pressure at time t, usually A-weighted for sound in air.

Sound exposure level

Sound exposure level (SEL) or acoustic exposure level is a logarithmic measure 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^[1]

L_{E}={\frac {1}{2}}\ln \!\left({\frac {E}{E_{0}}}\right)\!~{\mathrm {Np}}=\log _{{10}}\!\left({\frac {E}{E_{0}}}\right)\!~{\mathrm {B}}=10\log _{{10}}\!\left({\frac {E}{E_{0}}}\right)\!~{\mathrm {dB}},

where

E is the sound exposure;
E₀ is the reference sound exposure;
1 Np = 1 is the neper;
1 B = 1/2 ln 10 is the bel;
1 dB = 1/20 ln 10 is the decibel.

The commonly used reference sound exposure in air is^[2]

E_{0}=400~{\mathrm {\mu Pa^{2}\cdot s}}.

The proper notations for sound exposure level using this reference are L_{W/(400 μPa²⋅s)} or L_W (re 400 μPa²⋅s), but the notations dB SEL, dB(SEL), dBSEL, or dB_SEL are very common, even if they are not accepted by the SI.^[3]

References

↑ "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.
↑ Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
↑ 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), SP811 PDF

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