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).

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) 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 or, but the notations , , dBSEL, or dBSEL are very common, even if they are not accepted by the SI.