# Sound energy flux

Sound measurements
Characteristic
Symbol
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 flux is the flow rate of sound energy through a specified area.

## Mathematical definition

Sound energy flux, denoted Q and measured in W, is given by:[1]

$Q = \int_A p \mathbf v \cdot \mathrm d\mathbf A$

where:

• A is the area, measured in m2;
• p is the sound pressure, measured in Pa;
• v is the particle velocity, measured in m·s−1.

In a medium of density ρ for a progressive plane sound wave with speed c, the sound energy flux Q through a surface of area A with an angle θ between the direction of propagation of the sound and the normal to the surface, corresponding to an effective sound pressure p is:

$Q = \frac{p^2A} {{\rho}c}\cos{\theta}.$

For example a sound at SPL = 85 dB or p = 0.356 Pa in air (ρ = 1.2 kg·m−3 and c = 343 m·s−1) through a surface of area A = 1 m2 normal to the direction of propagation (θ = 0 °) has a sound energy flux Q = 0.3 mW.

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

## References

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