Acoustic Impedance - Complex Impedance

Complex Impedance

In general, a phase relation exists between the pressure and the particle velocity. The complex impedance is defined as

where

R is the resistive part, and

X is the reactive part of the impedance

The resistive part represents the various loss mechanisms an acoustic wave experiences such as random thermal motion. For the case of propagation through a duct, wall vibrations and viscous forces at the air/wall interface (boundary layer) can also have a significant effect, especially at high frequencies for the latter. For resistive effects, energy is removed from the wave and converted into other forms. This energy is said to be 'lost from the system'.

The reactive part represents the ability of air to store the kinetic energy of the wave as potential energy since air is a compressible medium. It does so by compression and rarefaction (expansion). The electrical analogy for this is the capacitor's ability to store and dump electric charge, hence storing and releasing energy in the electric field between the capacitor plates. For reactive effects, energy is not lost from the system but converted between kinetic and potential forms.

The phase of the impedance is then given by