## 2 Theoretical Background  
Some studies have approached the assessment of the acoustic quality of care facilities in terms of background noise levels monitoring [26; 27]. However, this work aims to make a further step: because speech-related functions are so important there, it is probably more appropriate to refer to parameters that can take into account (and parametrize) more factors at the same time, such as background noise levels, desired function (verbal communication in this case), room acoustics conditions (reverberation and volume), and occupancy. Acoustical capacity can serve this purpose: it was introduced as a concept in [PERSON]'s work about the acoustics of eating establishments and places for social gatherings in general [24; 28], and is defined as \"the maximum number of persons allowed in the room for _sufficientquality of verbal communication\" [29], where \"sufficient\" implies that the signal-to-noise ratio (SNR) is better than -3 dB, or that the ambient noise level does not exceed 71 dB. The concept of acoustical capacity relies on a prediction model reported in Equation (1) [24] for expected noise levels in the investigated eating facility, which is a function of the volume (\(V\)), the reverberation time (\(T_{0}\)) and number of people gathered in the room (\(N\))  
\[L_{\text{N,A}}=\frac{1}{1-c}\left(69-c\cdot 45-10\log\left(g\left(\frac{0.16 \cdot V}{T_{0}\cdot N}+Ap\right)\right)\right)\left(\text{dB}\right) \tag{1}\]  
where \(Ap\) is the sound absorption per person in m\({}^{2}\), \(c\) is the Lombard slope (dB/dB), and \(g\) is the group size, defined as the average number of people per speaking person (i.e., \(g=N/N_{\text{s}}\)). [PERSON] observed that, for the majority of eating establishments, the prediction model gives the most accurate results (within a range of \(\pm 2\) dB) with \(c=0.5\) dB/dB and \(A_{p}=0.2\) m\({}^{2}\). The main source of uncertainty indeed appears to be the group size parameter \(g\). The model reported in Equation (1) was validated using data from [PERSON] et al. [30], where a relatively broad range (in terms of number of seats, eating style, and physical and acoustic features) of eating establishments was considered.  
For the sake of generalizability, [PERSON] proposes a simplified relationship to calculate the acoustical capacity (\(N_{\text{max}}\)) based on (1)  
\[N_{\text{max}}\cong\frac{V}{20\cdot T} \tag{2}\]  
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. The formula (2) is obtained from the prediction model (1), based on a maximum ambient noise level of 71 dB (threshold for a sufficient quality of verbal communication), a slope value \(c=0.5\) dB/dB, a group size value \(g=3.5\) (average of the 3-4 N/N\({}_{\text{s}}\) range observed to work for most eating establishments), and an absorption per person value \(A_{p}=0.35\) m\({}^{2}\) (average of the 0.2-0.5 m\({}^{2}\) range observed to work for most eating establishments) [24; 29]. However, it was observed that depending on the type of gathering and social arousal, the parameter \(g\) could range from values as low as 2 (very lively gatherings), to 3-4 for more common settings (e.g., food courts, bistros, restaurants, etc.), up to more extreme situations of 8 for the dining rooms of residences for older adults. The focus of this paper is indeed on this latter case.