Physics:Sound exposure

Sound measurements
Characteristic	Symbols
Sound pressure	p, SPL,LPA
Particle velocity	v, SVL
Particle displacement	δ
Sound intensity	I, SIL
Sound power	P, SWL, LWA
Sound energy	W
Sound energy density	w
Sound exposure	E, SEL
Acoustic impedance	Z
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

[math]\displaystyle{ E = \int_{t_0}^{t_1} p(t)^2\, \mathrm{d}t, }[/math]

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

[math]\displaystyle{ 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}, }[/math]

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

[math]\displaystyle{ E_0 = 400~\mathrm{\mu Pa^2 \cdot s}. }[/math]

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.