## 6 Discussion  
A model is presented 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. An advantage of this approach is its interpretation of sound scattering due to interior equipment such as furniture, diffusors, or similar. The scattering effect is quantified in a parameter related to the energy transfer from the grazing to the non-grazing group. The parameter is denoted as the equivalent scattering absorption area \(A_{sc}\) and comprises the scattering and absorbent effect of interior objects in a room with a highly absorptive ceiling. Due to the presumption of an absorbent ceiling, the directional scattering effects of objects will appear. It is assumed that the ceiling absorption is much larger 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 [65]. There is an assumption concerning sufficiently great ceiling absorption to ensure that the energy reflected back to the non-grazing field can be neglected. It might also be of future interest to specify the conditions for a laboratory configuration as to how to estimate \(A_{sc}\). The methodology could be used to give input data for typical furnishing scenarios in different segments such as schools, offices, and healthcare premises. The directional effects of diffusors were studied in a classroom configuration by [PERSON] et al. [67]. In the presented model, it is assumed that the surface impedance is known or can be calculated for the suspended ceiling. Other surfaces are dealt with in a normal way using the practical or statistical absorption coefficients. Data for this can be found in handbooks in acoustics or manufactures' websites. The surface impedance is not a parameter normally provided by the manufacturers of absorbent ceilings. However, several examples of commercial software exist today that calculates the surface impedances for different types of absorbers. Figure 16: Measured and calculated reverberation times for case 1 and 2 in Table 2. Fifty mm and fifteen mm thick porous ceiling absorbers at a mounting height of 760 mm and 785 mm, respectively, were investigated. (Dashed green) 15 mm absorber, non-diffuse calculation; (solid green) 15 mm absorber, measurement; (dashed blue) 50 mm absorber, non-diffuse calculation; (solid blue) 50 mm absorber, measurement; (dashed red) 50 mm absorber, diffuse calculation; and (dash-dot red) 15 mm absorber, diffuse calculation. The need to include more complex boundary conditions for improved accuracy has also been noted in the development of simulation models [68]. Furthermore, the assumption of local reaction was investigated and the benefits of an extended reaction were shown to improve in accuracy, especially at lower frequencies [69]. In the model, the distance from the sound source to the receiver is a parameter. In this investigation, a representative value, see Equation (41), was used. For open-plan offices, it is of interest to calculate the sound propagation over distances corresponding, e.g., to different workplaces. As the model accounts for the distance and takes into account the angle-dependent absorption of the ceiling absorber, it would also be of interest to investigate this application. Another application where the non-diffuse sound fields appear are sport halls. A common treatment in such rooms is an absorbent ceiling. The present model clarifies the considerable deviation between diffuse field calculations and measurements that often appear in these rooms. It also shows the importance of a more uniform distribution of absorbent material. The general assumption of the SEA approach and the method for a subdivision into a grazing and non-grazing sound field can be further improved.