## 7 Conclusions  
A statistical energy analysis (SEA) model was developed for rooms with absorbent ceiling treatments. The model is based on a subdivision of the sound field into a grazing and non-grazing subsystem where grazing refers to sound waves propagating almost parallel to the absorbent ceiling. The scattering and absorbing effects of furniture and other interior objects is quantified in a measure denoted as the equivalent scattering absorption area \(A_{sc}\). This parameter is related to the energy transfer between the grazing and non-grazing subsystem. The back-transfer from the non-grazing to the grazing subsystem is assumed to be negligible. As a consequence, it is assumed that the ceiling absorption is much greater than the average absorption for walls and floors. An average absorption coefficient for the ceiling absorber greater than 0.7 for the octave bands ranging from 250 to 4000 Hz seems to be sufficient for most practical situations, but this has to be further investigated. In the model, it is assumed that the surface impedance for the suspended ceiling is known or can be calculated. Other surfaces are dealt with in the usual way, using the practical or statistical absorption coefficients. Based on the airflow resistance of the ceiling absorbers investigated, the surface impedances are estimated by the [PERSON]'s model, assuming an extended reaction. Thus, the actual mounting height of the ceiling absorber can be accounted for. The new model was compared with the classical diffuse field model. Experiments were carried out in a classroom mock-up. Two different ceiling absorbers for two different mounting heights were each investigated. One of these cases was also tested in combination with wall panels on two adjacent walls. For all the experiments carried out, the new model shows better agreement with measurements than the classical diffuse field model. The new model reproduces the frequency behaviour of the room acoustic parameters as well as accounting for wall panels in closer agreement with measurements than the diffuse field model. Further comparison with well-documented field measurements is necessary for the fine-tuning of the model, as well as investigation of the methodology used for estimating the equivalent scattering absorption area. Writing--original draft preparation, E.N. ; writing--review and editing, E.N. ; Experiments and investigations related to Sections 3.2.5 and 5.1, E.N. and E.A. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available on request from the corresponding author. The authors want to thank Ecophon R&D and Innovation for providing material, laboratory facilities and equipment. Thanks! The authors declare no conflict of interest. Derivation of the grazing angle at high frequencies. A more profound argumentation for the theory outlined in this appendix is given in [55,70]. We consider the rectangular room in Figure A1. From the wave equation, the complex wave number is given by  
\[\underline{k}^{2}=\underline{k}_{x}^{2}+\underline{k}_{y}^{2}+\underline{k}_ {z}^{2}\] (A1)  
and  
\[\cos(\theta)=\frac{k_{x}}{k}\] (A2)  
where \(k_{x}\) and \(k\) is the real part of \(\underline{k}_{x}\) and \(\underline{k}_{y}\) respectively. Near the absorbing ceiling we expect a phase step of nearly \(\pi\) for grazing incidence. This means that the real component of \(\underline{k}_{x}\) is approximately [55]  
\[k_{x}=\frac{\pi}{L_{x}}\bigg{(}n_{x}+\frac{1}{2}\bigg{)}\] (A3)  
where \(n_{x}\) is an integer 0, 1, 2...  
Equations (A2) and (A3) gives  
\[\cos(\theta)=\frac{c\pi}{\omega L_{x}}\bigg{(}n_{x}+\frac{1}{2}\bigg{)}\] (A4)  
\(\theta_{g}\) is defined by Equation (A4) for \(n_{x}=0\).