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

1. "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.
2. Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
3. 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