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Surface Impedance

Similar to the pressure reflection coefficient, the surface impedance can describe the changes in the magnitude and phase of a reflected pressure at the surface of interest. The real part of the surface impedance is called resistance, whereas the imaginary part is called reactance. The surface impedance is a less intuitive quantity, as defined by the following equation.

Z=(pvn)Z = (\frac{p}{v_n})

The inverse of the impedance is called surface admittance and describes how much the boundary "wants" the incident wave to enter.

Think of two extreme cases. When the wall is hard / rigid, the surface impedance goes to infinity as the air particle cannot move at a rigid surface. When the pressure is zero, then the surface impedance becomes zero too, and called pressure-release boundary condition.

As room acoustics generally deals with wave propagation in air, the normalized surface impedance (Z^\hat{Z}) is also often used, as ratio of the surface impedance to the characteristic impedance of air. As the normalized surface impedance approaches unity, the sound energy is more absorbed.

The relationship between the reflection coefficient and the surface impedance is as follows:

R(θ)=Zcos(θ)ρ0cZcos(θ)+ρ0c=Z^cos(θ)1Z^cos(θ)+1.R (\theta)= \frac{Zcos(\theta) -\rho_0 c}{Zcos(\theta) + \rho_0 c} = \frac{\hat{Z}cos(\theta)-1}{\hat{Z}cos(\theta)+1}.

The absorption coefficient is calcualted by the following equation:

α(θ)=1R(θ)2.\alpha (\theta)= 1 - |R(\theta)|^2.

where θ\theta is the angle of incidence.

The surface impedance can be measured directly in an impedance tube, for example, ISO 10534-2 [1], but unfortunately the availability of such data is scarce.


[1] ISO 10534-2:1998 Acoustics — Determination of sound absorption coefficient and impedance in impedance tubes — Part 2: Transfer-function method.