Sound energy flux

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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 exposure  E
 Sound exposure level  SEL
 Sound energy density  E
 Sound energy flux  q
 Acoustic impedance  Z
 Speed of sound   
 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.[1]

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 = \dfrac{p^2A} {{\rho}v}\cos{\theta}

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/m3; v=343 m/s; A=1m2;cos θ =1 ) has a sound energy flux of 0,3 mW


  1. ^ Landau & Lifshitz, "Fluid Mechanics", Course of Theoretical Physics, Vol. 6