Acoustic Energy Density

The two forms of energy in a wave are kinetic and potential. Denoting them at a particular time and position by and , respectively, we can write them in terms of velocity and wave impedance as follows:

More specifically, and may be called the acoustic kinetic energy density and the acoustic potential energy density, respectively.

At each point in a plane wave, we have (pressure equals wave-impedance times velocity), and so

where denotes the acoustic intensity (pressure times velocity) at time and position . Thus, half of the acoustic intensity in a plane wave is kinetic, and the other half is potential:^B.30

Note that acoustic intensity has units of energy per unit area per unit time while the acoustic energy density has units of energy per unit volume.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.