Sound energy density

Sound measurements
Characteristic	Symbols
Sound pressure	p, SPL
Particle velocity	v, SVL
Particle displacement	δ
Sound intensity	I, SIL
Sound power	P, SWL
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

$w = \frac{p v}{c}$

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).

Relationships with other quantities

Sound energy density is related to sound intensity:

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

where

• I is the sound intensity;
• c is the speed of sound.

Sound energy density is related sound power:

$w = \frac{P}{Ac},$

where

• P is the sound power;
• A is the area.

See also

• Particle velocity level
• Sound intensity level
• Sound energy density level

External links

• Conversion: sound intensity to sound intensity level
• Ohm's law as acoustic equivalent - calculations
• Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf