In german "Dämpfungskoeffizient" could be translated as 'damping coefficient' or 'deadening coefficient'. Ulf-J. Werner uses that to calculate the range of sound at different frequencies. This 'damping coefficient' being very low at low frequencies, rising with the frequenz in a logarithmic manner or in logarithmic proportion. So the 'absorption coefficient' is part of a formula to calculate 'sound transmission loss'.

The absorption is lineal while the TL is logarithmic that means that even a very important absorption it is a very low TL.

Furthermore the physical concept of absorption is to make disappear acoustic energy while the TL concept is to reflect the energy

Thanks.

In acoustic engineering, we usually differentiate. The applications are in fact different, room treatment is to guarantee acoustic comfort "inside" the room or cavity (for intelligibility for instance), while transmission applications aims at making sure you do not transmit the energy through the "walls" or panels. For "treatment" you typically want a material that absorbs sound (e.g. foam), while for "transmission" most of the time adding mass is key (but this will not improve the room treatment). So there are the materials used for "treatment" (with good absorption) and then those used to attenuate the "transmission" (with high transmission loss) - so there is a relation but not strict correspondence.

There is more than a relation between room acoustic and the physical composition: it is a real correspondence. – One example: A room with surrounding walls of stone with plaster (maybe with wallpaper on it, doesn't really matter). You will have a greater problem with deep frequences. Another room with walls of thin plaster plates (20 mm oder 25 mm), 50 – 80 mm mineral fleece, than again 20 - 25 mm plaster plate, and the next room. This to the right and left side + the wall to the floor. Deep frequences pass through the wall (the mineral fleece does only matter very less) and in result you have less problems or maybe no problems with deep frequences inside your room. Room acoustic is directly corresponding with physical aspects of the building. And you will have (nearly) NO chance to correct the problem with disturbance in the neighbour rooms by noise in the area of deep frequences. – Nevertheless you CAN create a good speech intelligibility and clarity of sound INSIDE the room. So or so (with thin walls of plaster plates or heavy stone walls) there is a possibility to create a good room acoustic parallel to a bad constitution of the building (causing disturbance from outside). This is (so I think) what you mean, when saying that there is a "relation but not strict correspondence" between room acoustic and the pysical behavior of a building.

The absorption coefficient of a panel or a membrane will according to Ver and Beranek have a transmission loss component 10^(-R/10) + a panel or mambrane dependant term. It is briefly described in this article draft with the reference: Preprint On sound absorption in panels, wall linings and wood floors ...

This may be relevant eg for outdoor «stage bubbles», »bubble tennis courts», tents, or simply for light walls with somewhat low sound insulation. At low frequencies the transmission term of the »absorption» may be 0,1 or even higher.