## 4 Results
### Acoustical Capacity Pre- and Post-Intervention  
As mentioned in the Introduction, [PERSON] [28; 29] suggests that, for a room with known physical and room acoustics characteristics, it is possible to estimate the maximum number of persons--i.e., the acoustical capacity (\(N_{\text{max}}\))--in order to have a sufficient quality of verbal communication by means of Equation (2). However, the formula (2) assumes \(A_{p}\) = 0.35 m\({}^{2}\) and \(g\) = 3.5, whilst the analysis reported in Section 4.2 shows that, for the specific case of a NH hosting people with BPSD among other residents, the most accurate set of parameters to feed into the model was: \(A_{p}\) = 0.2 m\({}^{2}\) and \(g\) = 9. Furthermore, it would not be accurate to assume 71 dB as the threshold value for sufficient quality of verbal communication for the particular group of users of this case study. The relationship between speech level (\(L_{\text{S,A,1m}}\)) and ambient noise level (\(L_{\text{N,A}}\)) has been extensively discussed in the literature [25; 37]: considering the relation between these two parameters in terms of signal-to-noise ratio (SNR), [PERSON] [38] suggests that for a reference listener, the quality of verbal communication is sufficient if SNR \(>\) -3 (\(L_{\text{N,A}}\) < 71 dB). Nevertheless this criterion should apply only for normal hearing people, and the ISO 9921:2003 reports that _\"people with a slight hearing disorder (in general older people) or non-native listeners require a higher signal-to-noise ratio (approximately 3 dB)\"_[39]. This implies that in the case of an NH, where profound rather than slight hearing disorder is likely to affect many residents, the most appropriate choice could indeed be an even higher SNR than the 0 dB (\(L_{\text{N,A}}\) < 65 dB) recommended by the ISO [40]. For this reason, a condition with SNR \(>\) 3 dB (\(L_{\text{N,A}}\) < 59 dB) was considered to reflect a \"sufficient\" quality of verbal communication for this group \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{_c_ (dB/dB)} & \multicolumn{3}{c}{**Average Deviation (dB)**} \\ \cline{2-4}  & \multicolumn{3}{c}{**Group Size, \(g\)**} \\ \cline{2-4}  & 8 & 9 & 10 \\ \hline
0.4 & 1.8 & 2.7 & 3.4 \\
0.5 & \(-\)0.8 & 0.3 & 1.2 \\
0.6 & \(-\)4.6 & \(-\)3.3 & \(-\)2.2 \\
0.7 & \(-\)11.1 & \(-\)9.4 & \(-\)7.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average deviations between predicted and measured noise levels in the living room, using \(A_{p}\) = 0.2 m\({}^{2}\) and different values for the parameters \(c\) and \(g\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{_A\({}_{p}\)_(m\({}^{2}\))} & \multicolumn{3}{c}{**Average Deviation (dB)**} \\ \cline{2-4}  & \multicolumn{3}{c}{**Group Size, \(g\)**} \\ \cline{2-4}  & 8 & 9 & 10 \\ \hline
0.2 & \(-\)0.8 & 0.3 & 1.2 \\
0.3 & \(-\)0.6 & 0.4 & 1.4 \\
0.4 & \(-\)0.4 & 0.6 & 1.5 \\
0.5 & \(-\)0.3 & 0.8 & 1.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average deviations between predicted and measured noise levels in the living room, using \(c\) = 0.5 dB/dB and different values for the parameters \(A_{p}\) and \(g\). of users. Figure 4 reports a comparison between these three conditions, where a 3-dB and a 6-dB shift can be observed for slight and profound hearing disorders, accordingly, in the assessment of quality of verbal communication. Therefore, assuming the new set of parameters, considered at the sufficient quality level for profound hearing disorder, the revised relationship for acoustical capacity in Nursing Homes (NH) would result in  
\[N_{\text{max,NH}}\cong\frac{V}{33.6\cdot T} \tag{3}\]  
where \(V\) is the volume in m\({}^{3}\) of the room and \(T\) is the reverberation time (s) in furnished but unoccupied condition at mid-frequencies. Using the formula (3), the acoustical capacity of the NH living room prior to the acoustical retrofit interventions can be calculated and it is \(N_{\text{max,NH}}\) = 20.