Simcenter 3D Solutions How to convert an absorption coefficient to an impedance?
Summary
In many applications, we need to apply an absorbent material to decrease the sound level. To model and to consider this material effect, you have 3 methods: 1. To use a porous material: generally, the material supplier will not give you all needed parameters and to obtain them you have to use some specific test processes or to work with laboratory which are able to measure all porous parameters. 2. To use transfer functions between the 2 sides of the absorbent material: it can be obtained using measurements. 3. To use an absorber to be able to apply an impedance: generally, the material supplier will not give you the impedance, but the absorption coefficient. In this document, you will find a method to convert an absorption coefficient to an impedance.
Details
Material suppliers can give you absorption coefficient data.
There is a relation between the absorption coefficient and the impedance:
You can find it in the acoustic user guide: https://docs.sw.siemens.com/en-US/doc/289054037/PL20221116635356703.acoustic/xid1058541.
In our case, we will consider only normal waves : it means Zi = 0 kg/(m².s)
We obtain : 
Zr² + 
Zr + α = 0
Zr² + 
Zr + 
= 0
= 0
We can calculate the determinant: determinant = b² - 4.a.c = Δ
Where : a = α ; b = 
; c = 
Then Δ = 16.
As α ≤ 1 we can conclude that Δ will always be positive.
With the last formula, you can calculate Zr with the 2 next formulas:
Zr1 = 
Zr2 =
Now you can calculate impedances corresponding to an absorption coefficient curve.
Generally, we prefer to use Zr2: it gives more accurate results.