Sound exposure

Template:Sound measurements 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

$E=\underset{t_0}{\overset{t_1}{\int }}p(t{)}^2\mathrm{d}t,$

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) 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

$L_E=\frac{1}{2}\ln \left(\frac{E}{E_0}\right)\mathrm{N}\mathrm{p}={\log }_{10}\left(\frac{E}{E_0}\right)\mathrm{B}=10{\log }_{10}\left(\frac{E}{E_0}\right)\mathrm{d}\mathrm{B},$

where

• E is the sound exposure;
• E₀ is the reference sound exposure;
• Template:Nowrap is the neper;
• Template:Nowrap is the bel;
• Template:Nowrap is the decibel.

The commonly used reference sound exposure in air is

$E_0=400\mathrm{\mu }\mathrm{P}{\mathrm{a}}^{\mathrm{2}}\mathrm{\cdot }\mathrm{s}.$

The proper notations for sound exposure level using this reference are Template:Nobreak or Template:Nobreak, but the notations Template:Nobreak, Template:Nobreak, dBSEL, or dB_SEL are very common, even if they are not accepted by the SI.