Sound energy density

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Not to be confused with Sound pressure.
Sound measurements
 Sound pressure  p · SPL
 Particle velocity  v · SVL
 Particle displacement  ξ
 Sound intensity  I · SIL
 Sound power  P · SWL
 Sound energy  W
 Sound energy density  w
 Sound exposure  E · SEL
 Sound energy flux  Q
 Acoustic impedance  Z
 Speed of sound  c
 Audio frequency  AF

Sound energy density or sound density (symbol w) describes the sound energy per volume unit at a given point in the medium.

Mathematical definition[edit]

Sound energy density, denoted w and measured in J·m−3 or Pa, is given by:

w = \frac{p v}{c}


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).

Equations in terms of other measurements[edit]

Sound energy density can be related to other sound measurements:

w = \frac{p^2}{c \mathfrak{R}(z)} = \frac{\mathfrak{R}(z) v^2}{c} = \frac{P}{c A} = \frac{I}{c}.

For sine waves with angular frequency ω, the amplitude of the sound energy density can be related to those of the particle displacement and the particle acceleration:

w_\mathrm{m}(\mathbf r) = \frac{\omega^2 z_\mathrm{m}(\mathbf r) \xi_\mathrm{m}(\mathbf r)^2}{c} = \frac{z_\mathrm{m}(\mathbf r) a_\mathrm{m}(\mathbf r)^2}{c\, \omega^2}.
Symbol Unit Meaning
c m·s−1 speed of sound
v m·s−1 particle velocity
z Pa·m−1·s specific acoustic impedance
A m2 area
p Pa sound pressure
P W sound power
I W·m−2 sound intensity
w J·m−3 sound energy density
ω rad·s−1 angular frequency
ξ m particle displacement
a m·s−2 particle acceleration

See also[edit]

External links[edit]