# Sound energy density

Sound measurements
Characteristic
Symbol
Sound pressure  p · SPL
Particle velocity  v · SVL
Particle displacement  ξ
Sound intensity  I · SIL
Sound power  Pac
Sound power level  SWL
Sound energy
Sound exposure  E
Sound exposure level  SEL
Sound energy density  E
Sound energy flux  q
Acoustic impedance  Z
Speed of sound
Audio frequency  AF

The sound energy density or sound density (symbol E or w) is an adequate measure to describe the sound field at a given point as a sound energy value. The letter "lower case w" sign $w$ is easily mixed with the sign $\omega$ (omega), therefore we choose the letter E.

In opposite to the sound intensity I, which gives the sound power per area A, the sound energy density E (also: sound density) describes the time medium value of the sound energy per volume unit; it gives information about the sound energy which is at a defined place in the room.

The sound energy density E (or w) for an even-proceeding sound wave is:

$E = \frac{I}{c}$,

where I is the sound intensity in W/m2 and c is the sound speed in m/s.
The sound energy density is given in J/m3, where the joule J = W·s = N·m.
You will find also W·s/m3 or N·m/m3.
The unit of measurement for sound energy density is N/m2, also known as pascals, the same as the units of sound pressure.

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).

More formulas for sound energy density for even proceeding sound waves:

$E = \xi^2 \cdot \omega^2 \cdot \rho = v^2 \cdot \rho = \frac{a^2 \cdot \rho}{\omega^2} = \frac{p^2}{Z \cdot c} = \frac{I}{c} = \frac{P_{ac}}{c \cdot A} = \frac{I}{f \cdot \lambda}$

where:

Symbol Units Meaning
p pascals sound pressure
f hertz frequency
ξ m, meters particle displacement
c m/s speed of sound
v m/s particle velocity
$\omega$ = 2 · $\pi$ · f radians/s angular frequency
ρ kg/m3 density of air
Z = c · ρ N·s/m³ acoustic impedance
a m/s² particle acceleration
I W/m² sound intensity
E W·s/m³ sound energy density
λ m wavelength
Pac W, watts sound power or acoustic power
A area

For digits of the sound energy density the RMS value will be given.
But you get also the level in dB. See sound energy density level.