## 4 Results and Discussion
### Facades with Two Walls and a Roof  
The facade attenuation for a room having two vertical walls and a four-pitched roof was also investigated. Rooms with plan dimensions ranging from 3 m \(\times\) 3 m to 6 m \(\times\) 6 m were considered. The center of the facades was considered at heights of 1, 4, 7 and 10 m. The overall average results are summarized in Table 4.  
It is worth noting that the attenuations computed for the roof are similar in the different cases if the loudspeaker is positioned in such a way that it is \"in view\" of one or of two walls (only floor F0 and F1). The attenuations related to the walls are similar to the case with two walls for the ground and the first floor (see Table 2). The maximum variation of the attenuation due to the diffraction as a function of the width of the room is 1.7 dB for the walls and 2.3 for the roof. The minimum attenuations for positions A-B-C-D are 20.3 dB, 18.5 dB, 15.8 dB and 14.5 dB for floors F0, F1, F2 and F3 respectively. The minimum attenuations of the roof are 11.0 dB, 16.9 dB, 18.4 dB and 15.4 dB, respectively. These attenuations are larger if compared to the ones reported for the case of a two-pitched roof because the four-pitched roof has about half of the surface subject to a double diffraction.  
Some results, expressed as one octave band attenuations due to the diffractions of the different items (corner, roof edge), are reported in Appendix A in the case of corner rooms and rooms featuring  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** \\ \cline{2-9}  & **3 x 6-6 x 6** & **3 x 5-6 x 5** & **3 x 4-6 x 4** & **3 x 3-6 x 3** & **3 x 6-6 x 6** & **3 x 5-6 x 5** & **3 x 4-6 x 4** & **3 x 3-6 x 3** \\ \hline \multirow{2}{*}{F0} & _22.0–23.6_ & _21.4–23.1_ & _20.9–22.5_ & _20.3–21.6_ & _1.0–2.5_ & _0.4–1.8_ & _1.7–2.5_ & _0.9–2.0_ \\ \cline{2-9}  & **11.8–14.1** & **11.5–13.7** & **11.2–13.5** & **11.0–13.2** & **11.3–13.5** & **11.9–13.9** & **12.1–14.0** & **11.8–13.7** \\ \hline \multirow{2}{*}{F1} & _20.2–21.8_ & _19.7–21.3_ & _19.2–20.8_ & _18.5–20.0_ & _9.5–11.2_ & _3.3–4.3_ & _1.0–2.2_ & _1.4–2.3_ \\ \cline{2-9}  & **17.6–19.8** & **17.6–19.8** & **16.9–19.2** & **17.2–19.2** & **17.2–19.5** & **17.6–19.8** & **17.1–19.3** & **17.8–19.9** \\ \hline \multirow{2}{*}{F2} & _15.8–17.4_ & _17.0–18.4_ & _16.6–17.1_ & _16.0–17.3_ & - & - & - & - \\ \cline{2-9}  & **18.4–20.6** & **18.5–20.7** & **18.6–20.8** & **18.6–20.8** & - & - & - & - \\ \hline \multirow{2}{*}{F3} & _15.9–17.1_ & _15.4–16.6_ & _15.0–16.2_ & _14.5–15.7_ & - & - & - & - \\ \cline{2-9}  & **17.6–19.5** & **17.5–19.4** & **15.4–17.6** & **16.4–18.5** & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Unweighted global attenuation range \(\Delta\)D\({}_{\rm FL}\) [dB] of walls (italic font) and roof (bold font).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **3 x 6-6 x 6** & **3 x 5-6 x 5** & **3 x 4-6 x 4** & **3 x 3-6 x 3** \\ \hline F0 & 10.8–12.4 & 10.7–12.3 & 10.7–12.3 & 10.5–12.2 \\ \hline F1 & 16.9–18.3 & 16.9–18.4 & 16.8–18.3 & 16.7–18.2 \\ \hline F2 & 16.4–17.8 & 16.4–17.9 & 16.4–17.8 & 16.3–17.7 \\ \hline F3 & 15.5–16.8 & 15.5–16.8 & 15.4–16.8 & 15.4–16.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Unweighted global attenuation range \(\Delta\)D\({}_{\rm 31}\) [dB].  
a rooftop. The values reported in the graphs can be used as a reference to estimate the attenuations of real cases.