Sound exposure

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Sound measurements
 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[edit]

Sound exposure, denoted E, is defined by

E = \int_{t_0}^{t_1} p(t)^2\, \mathrm{d}t,


  • 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[edit]

For other uses, see Sound 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[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},


  • 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 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.[3]


  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