Combining sound absorption coefficients

Question

I am trying to predict the reverberation time in a room with different surfaces and different absorption coefficients (i.e. curtains, wood panels, carpet etc). My question is about how to calculate the overall absorption coefficient and area of absorption if you have two different layers of material? For example:

If there is a curtain with an absorption coefficient of 0.5 @ 500Hz, hanging in front of a wall with an absorption coefficient of 0.2 @ 500Hz, how do i find the overall absorption coefficient and area of absorption?

Thanks for your help, Jaryd

Answer 1

You could use the transfer matrix method. It is commonly used to model propagation of sound in porous materials.

Answer 2

User77601 is correct regarding the transfer matrix method. Most probably it would provide some reasonably good results and they will, most probably, be better than just assuming that the sound will be affected equally by both surfaces.

You have to keep in mind though that you should include the air gaps between the materials if this is possible. It's understandable though that curtains (and many other objects/materials) don't have a constant distance from adjacent surfaces and this may need some trial-and-error approach to get correct results. Nevertheless, it will provide better results than a naive approach of weighting all the absorption coefficients equally.

For a quite nice introduction to the transfer matrix method (as well as to absorption in general), you can refer to "Acoustic Absorbers and Diffusers - Theory, Design and Application" by Cox and D'Antonio. Additional information can be found in "Application of Transfer Matrix Method in Acoustics" by Campa and Camporeale, as well as Transfer Matrix Method page in Wikipedia.