Sound exposure explained

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 _{1}} _{t _{0}} p(t) ^{2} 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^[1]

L _{E} = (1)/(ln \left( 2) (E)/(E _{0}) \right)~ Np = log _{10} \left( (E)/(E _{0}) \right)~ B = 10 log _{10} \left( (E)/(E _{0}) \right)~ dB , where

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

The commonly used reference sound exposure in air is^[2]

E _{0} = 400 ~ \muPa ^{2} ⋅ s . The proper notations for sound exposure level using this reference are or, but the notations,, dBSEL, or dB_SEL are very common, even if they are not accepted by the SI.^[3]

Notes and References

1. http://webstore.iec.ch/webstore/webstore.nsf/artnum/028981 "Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units"
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