## 5 Application in a Case Study: Use of MPPs as a Ceiling Acoustic Treatment  
A wide employment of sustainable materials such the multi-layer MPPs analyzed in this study is expected to occur in several typologies of enclosed environments [35, 43], replacing or integrating the common sound absorbing treatments. MPP absorbers are theoretically expected to return the same acoustic behavior regardless of their constitutive material. Therefore, concerning sustainability aspects, they can be made of any green material, reducing the environmental footprint of the whole process. The acoustic simulation of a wide application in a 3D virtual enclosure is a useful tool in a preliminary step in the assessment of their performance [44, 45, 46]. Figure 13: Two possible stencils: standard 7-point (**left**) and cubic close-packed (CCP) 13-point (**right**). Image credit: see reference [28]. With this purpose, the acoustic condition of a large university lecture hall has been simulated with a ceiling-mounted system of double-layer MPPs. Such a kind of large rooms shows the highest values of reverberation time at 500 and 1000 Hz (see Figure 4 in [27]), the same frequency range occupied by the human voice [47]. As too high values of reverberation time deteriorate speech intelligibility, a material whose sound absorbing properties are mostly centered in such a frequency range may return useful outcomes in acoustic treatments of existing university halls. Otherwise, an acoustic treatment with porous or fiber materials would provide the most significant absorbing contribution at higher frequencies [48], sometimes entailing too dry conditions at 2000 Hz and 4000 Hz. The room chosen as a case study is a historical lecture hall in the University of Bologna (see Figure 14). A previous campaign of acoustic measurements [27; 49] in the hall allowed to collect the main room criteria [50] and intelligibility indexes [47]. The setting of sound source and receiver locations chosen for the measurements campaign is also provided in Figure 14.  
The 3D virtual model of the hall-about 900 m\({}^{3}\) was built with Sketchup [51] according to consolidated approximation guidelines (see Figure 15), i.e., with a certain degree of geometrical approximation and with a proper division in macro-layers depending on the materials [52; 53]. The 3D model was modeled using a small group of different materials (see Table 5) to reduce the uncertainties underlying the assignment of material properties to each surface. With regard to the absorption area distribution, it should be noted that, generally, the seats are the most sound absorbing objects in a lecture hall in unoccupied state [23; 44; 45; 46]. The remaining layers of the model (walls, floor, ceiling) are made up of rather hard and reflective surfaces, and thus they show low values in the whole frequency range. It should also be highlighted that the random incidence absorption coefficients at low frequencies of wooden parts are due to the air cavity behind them (see dataset in Table 5). The state-of-the-art procedure to simulate the sound field of a large lecture hall would imply the use of geometrical acoustics (GA) techniques [46; 54]. Nevertheless, MPPs are not suitable to be characterized by the energy-based parameters, i.e., the absorption coefficients, usually involved in GA practice. Therefore, the need arose to simulate the acoustic behavior by using a wave-based algorithm, such as a FDTD model, that, additionally, assures the correct computation of the diffraction effects due to the objects' edges [55]. Figure 14: Interior view (**left**) and 2D plan (**right**) of the lecture hall under study. Sound sources (S1, S2) and the spatial grid of microphone receivers (R1, R2,..., RN) used in the measurements campaign are reported. With this purpose, in the 3D virtual model the edges of the blocks containing the seats and the long tables were modeled (see Figure 16b).