# Comfort Distance--A Single-Number Quantity Describing Spatial Attenuation in Open-Plan Offices
###### Abstract
It should be noted that \(d_{\text{C}}\) is not an alternative quantity of distraction distance \(r_{\text{D}}\) since \(d_{\text{C}}\) is purely based on spatial attenuation of speech and it ignores the background noise level of the room, unlike \(r_{\text{D}}\). However, their approach did not gain support at that time since there was too little published evidence about the suitable \(d_{\text{C}}\) values, and it was also based on \(DL_{t}\) which was already discarded in ISO 3382-3. Furthermore, there was already some uncertainty about the acceptance of \(r_{\text{D}}\) among acousticians and non-acousticians. It was found safer to limit the distance-related SNQs to \(r_{\text{D}}\) and \(r_{\text{P}}\), which were derived from the spatial decay of \(STI\). Authors' interactions with non-acousticians have learned that privacy-related SNQs, i.e., \(r_{\text{D}}\) and \(r_{\text{P}}\), have been well understood. An important reason for this was a study, which showed that cognitive performance deteriorates with increasing \(STI\), i.e., with reducing speech privacy [12]. A later important reason was a cross-sectional study showing that shorter \(r_{\text{D}}\) was associated with a lower probability of being highly disturbed by office noise [3]. Against expectations, \(D_{2,5}\) did not show any association with that probability. The most probable reason is that the latter ignores the effect of background noise (masking). Authors' experience has been that the attenuation-related SNQs, i.e., \(D_{2,5}\) and \(L_{\text{p,A,S,4m}}\), have been more difficult to understand by non-acousticians. The reason for this is that both quantities have the same unit but different definitions. It would be useful to have a simpler attenuation-related SNQ to facilitate communication with non-acousticians. [PERSON] et al. [13] described the room acoustic properties of their open-plan offices by comfort distance as introduced by [PERSON] and [PERSON] [11]. They defined the comfort distance as the distance where the A-weighted SPL of speech falls below \(L_{\text{p,A,C}}=48\) dB. However, the comfort criterion level, \(L_{\text{p,A,C}}\), was not based on a thorough analysis of the existing measurement data. The A-weighted SPL of speech, \(L_{\text{p,A,S}}\) depends linearly on logarithmic distance, \(r\), from the speaker. Therefore, \(L_{\text{p,A,S}}\) can be determined from the linearly fitted SNQ values of ISO 3382-3 by  
\[L_{\text{p,A,S}}=L_{\text{p,A,S,4m}}+2D_{2,5}-\frac{D_{2,5}}{\log_{10}(2)} \cdot\log_{10}(r) \tag{1}\]  
If \(L_{\text{p,A,S}}\) equals the comfort criterion level, \(L_{\text{p,A,C}}\), the distance \(r_{\text{C}}\), where this is achieved, i.e., comfort distance, gets a general form:  
\[r_{\text{C}}=2^{(L_{\text{p,A,S,4m}}-L_{\text{p,A,C}}+2\cdot D_{2,5})/D_{2,5}} \tag{2}\]  
This form was recently used by [PERSON] et al. [7]. They set the comfort criterion level to \(L_{\text{p,A,C}}=45\) dB. However, they did not describe the origin of that choice. Most importantly, the comfort distance can be calculated by the SNQs which are already determined in ISO 3382-3. Some countries already have mandatory target values or voluntary classification systems for the room acoustic quality of open-plan offices using the SNQs of ISO 3382-3 [14; 15]. It would be useful to find suitable limiting values for the acoustic classes A-D also for comfortable distance. Because \(r_{\rm C}\) belongs among the key SNQs in the draft international standard ISO DIS 3382-3 [16], the elaboration of the scientific basis of \(r_{\rm C}\) is justified. The purpose of our study is to present the scientific basis of comfort distance to better introduce it as a new SNQ in the revised version of ISO 3382-3 [6; 16]. The second purpose was to compare the ISO 3382-3 [6] data reported in previous studies to calculate the range of typical comfort distance values using Equation (2). The third purpose was to propose limit values for the classification of comfort distance based on all available data.