Communication presented at the 17th International Congress on Acoustics, Rome, 2-7 September 2001.This paper presents a theoretical and experimental study that shows the presence of a horizontal asymptote of the absorption coefficient function α(f) in relation with the thickness of the sample. This asymptote conduces to the existence of a critical depth, characterized by a certain attenuation of the sound wave, that limits the absorbing properties of the material. Above this thickness, α(f) does not change noticeably and a progressive increase of the layer thickness only means an unnecessary waste of acoustic material.This work has been partially supported by the National Research and Development (R&D) Program within the Project AMB..98-1029-C04-01.Peer reviewed