# Comfort Distance--A Single-Number Quantity Describing Spatial Attenuation in Open-Plan Offices
###### Abstract
This guarantees that different operators obtain similar measurement results from the same office as shown by the Round Robin test of [PERSON] et al. [7]. [PERSON] et al. [8] reported measurement results from the office where the background noise level, \(L_{\text{P,A,B}}\), varied even 13 dB within a single measurement path. ISO 3382-3 [6] states that the mean of \(L_{\text{P,A,B}}\) values along the measurement positions shall be used in the position-dependent \(STI\) determinations. In such special cases, the uncertainty of \(r_{\text{D}}\) and \(r_{\text{P}}\) may be higher than in the Round Robin test of [PERSON]. [7] where the spatial distribution of background noise was smooth. ISO 3382-3 [6] was largely based on the method described by [PERSON] et al. [9], who studied 15 different open-plan offices. An extended version involving 16 offices was published later by [PERSON] et al. [5]. They suggested the abovementioned SNQs that deal with spatial decay instead of temporal decay of sound since reverberation time was not associated with spatial decay rate in a non-diffuse sound field. Therefore, reverberation time did not belong to the reported SNQs of ISO 3382-3. Furthermore, they showed that the A-weighted SPL of speech was usually linearly associated with logarithmic distance. Because speech is the main noise source in offices, it was justified to focus on the spatial decay of A-weighted SPL of speech. ISO 14257 [10] was an important role model in the development of ISO 3382-3 because the new quantities were revolutionary at that time when most room acousticians were used to measuring reverberation time and background noise levels in the first place. ISO 14257 [10] was among the first acoustic standards that focused on a non-diffuse sound field. It involved two SNQ's that were considered during the standardization of ISO 3382-3: rate of spatial decay of SPL per distance doubling, \(DL_{2}\) [dB], and excess of SPL, \(DL_{\ell}\) [dB]. The latter describes how much the spatial decay rate deviates from the free field. However, these quantities were determined in octave bands. Such a large amount of  
Figure 1: A-weighted SPL, \(L_{\text{P,A}}\), as a function of distance, \(r\), to the speaker (black circles) and a linear fit over the data (dashed line). Definitions for \(D_{\text{2,S}}\), \(L_{\text{P,A,S,4m}}\), and \(r_{\text{C}}\) are given in Section 1. The data is not related to this study. reported outcomes did not serve the purpose of ISO 3382-3 of providing simple and scarce SNQs as the main outcomes. Because it was evident from office surveys that speech is the main noise source, and that speech has a standardized spectrum shape and overall level, the approach of using A-weighted SPL of speech was justified. This led to the definition of \(D_{2,5}\) as a primary quantity describing the spatial decay rate. However, it was not alone sufficient to describe the spatial decay since the sound attenuation in the nearfield varies a lot between offices due to different room height, screen height, and room absorption. Therefore, \(L_{\text{p,A,S,4m}}\) was chosen to be used as an anchor point for \(D_{2,5}\) slope instead of \(DL_{t}\), since the former was easier to understand and determine. It should be noted that the SNQs of ISO 3382-3 had to be understandable also among non-acousticians involved with office design, such as building owners, workplace designers, material and furniture providers, authorities, facility managers, occupational physicists, ergonomists, HR people, managers, and office users. During the standardization process, which lasted from 2009 to 2012, [PERSON] and [PERSON] [11] proposed an alternative option to \(L_{\text{p,A,S,4m}}\) and \(DL_{t}\): the distance of comfort, \(d_{\text{C}}\) [m]. It was the distance, where an acceptable A-weighted SPL of speech was achieved.