Partition Impedance of Orifices

The method of equivalent networks was originally designed for a sequence of layers without constrictions. The impedance at a layer boundary is defined by the ratio of sound pressure p and normal velocity v, both averaged over the boundary surface S, $Z={\langle p\rangle _{S}}/{\langle v\rangle _{S}}$. A layer with constrictions (e.g. a plate with the neck of a resonator) can be included in the equivalent network scheme if an orifice partition impedance (or simply: orifice impedance) Z${}_{{M}}$ is added to the orifice of the constriction. This is a partition impedance of the type $Z_{p}={\langle\Delta p\rangle _{S}}/{\langle v\rangle _{S}}$ with $\Delta p=(p_{{front}}-p_{{back}})$ the sound pressure drop across the plane of the orifice and v the particle velocity through the orifice (in the direction front$\to$back).

Assume the area of the orifice is s (e.g. $s=$ the cross-section area of a neck) with the porosity $\sigma=s/S$ (e.g. $S=$cross-section area of a single...