# Sound energy density

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
Speed of sound  c
Audio frequency  AF
Transmission loss  TL

Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), that is the joule per cubic metre (J/m3) in SI based units.

## Mathematical definition

Sound energy density, denoted w, is defined by

${\displaystyle w={\frac {pv}{c}}}$

where

The terms instantaneous energy density, maximum energy density, and peak energy density have meanings analogous to the related terms used for sound pressure. In speaking of average energy density, it is necessary to distinguish between the space average (at a given instant) and the time average (at a given point).

## Sound energy density level

The sound energy density level gives the ratio of a sound incidence as a sound energy value in comparison to a reference level of 0 dB (DIN 45630). It is a logarithmic measure of the ratio of two sound energy densities.

The energy produced by vibrations is known as sound

${\displaystyle L(E)=10\,\log _{10}\left({\frac {E_{1}}{E_{0}}}\right){\rm {dB}}}$

where E1 and E0 are the energy densities. The unit of the sound energy density level is the decibel (dB).

If E0 is the standard reference sound energy density of[1]

${\displaystyle E_{0}=10^{-12}\mathrm {\frac {J}{m^{3}}} }$