Sound energy density

Not to be confused with Sound pressure.

Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), which is 1 kg⋅m⁻¹⋅s⁻² in SI base units or 1 joule per cubic metre (J/m³).^{[1]: Section 2.3.4: Derived units, Table 4}

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
v t e

Mathematical definition

Sound energy density, denoted w, is defined by

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

where

• p is the sound pressure;
• v is the particle velocity in the direction of propagation;
• c is the speed of sound.

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 the reference level of 1 pPa (= 10⁻¹² pascals).^[2] It is a logarithmic measure of the ratio of two sound energy densities. The unit of the sound energy density level is the decibel (dB), a non-SI unit accepted for use with the SI Units.^{[1]: Chapter 4: Non-SI units that are accepted for use with the SI, Table 8}

The sound energy density level, L(E), for a given sound energy density, E₁, in pascals, is

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

where E₀ is the standard reference sound energy density^[3]

${\displaystyle E_{0}=10^{-12}\ \mathrm {Pa} }$ .

See also

• Particle velocity level
• Sound intensity level