# Sound exposure

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

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

## 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 LE and measured in dB, is defined by

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

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

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

The proper notations for sound exposure level using this reference are LW/(400 μPa2⋅s) or LW (re 400 μPa2⋅s), but the notations dB SEL, dB(SEL), dBSEL, or dBSEL are very common, even if they are not accepted by the SI.