Sound energy flux

Sound measurements
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 energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c
Audio frequency AF

Sound energy flux (the energy produced by an object's vibrations, symbolized as q) results from the integral of the acoustic pressure p times the particle velocity v over a surface A , and is given by the integral below.

$q = \int (p\vec{v}) \cdot \mathrm{d}\vec{A}$

The sound energy flux is the average rate of flow of sound energy for one period through any specified area A and is usually referred to as acoustic intensity.

In a medium of density ρ for a plane or spherical free wave having a velocity of propagation v, the sound energy flux through the area A corresponding to an effective sound pressure p is

J = (p²A / ρ v) cos θ

where θ = the angle between the direction of propagation of the sound and the normal to the area A.

This is the parameter one would be interested in when converting noise back into usable energy, along with any losses in the capturing device.

For example a sound at 85 dB or 0,356 Pa in air (ρ=1,2 kg/m²; v=343 m/s; A=1m²;cos θ =1 ) has a sound energy flux of 0,3 mW