The auditory perceived aperture position of the transition between rooms

The human auditory system derives important spatial cues from the acoustics of a room. Reverberation allows listeners to perceive their position, distance of sound sources, and even infer geometry and size of the space (Khaykin and Rafaely, 2012). When a receiver or listener moves inside a room, several characteristics change, such as direct-to-reverberant ratio (DRR), early reflections, and modal coupling, while reverberation time remains largely constant. However, when coupled spaces are considered, acoustical features such as double-slope decays, boundary diffraction, and portalling effects emerge (Billon et al., 2006; Eyring, 1931; Xiang et al., 2009). All of these vary with inter-room position and coupling aperture size (Harris and Feshbach, 1950; Luizard and Katz, 2014), while perceptual effects include abrupt changes in reverberance, envelopment, and image shifting. The transition between rooms is therefore a highly complex interaction (Luizard et al., 2015b). While some research has been undertaken to understand the effects of coupling aperture size on propagation and diffusion effects of coupled rooms (Luizard and Katz, 2014; Xiang et al., 2013) as well as the perception of double-slope decays (Ermann, 2007; Luizard et al., 2015b), little has been published on the perceptual experience of travelling between two adjoined rooms.

In a previous study investigating the acoustics of coupled room transitions, the direction and intensity of reflections were shown to change rapidly at locations close to the coupling aperture (McKenzie et al., 2021a). In simple audio engines and auralisation methods, a room transition may simply switch or linearly fade between the reverberation of the two rooms, which is insufficient for immersive and realistic applications (McKenzie et al., 2021b). This study establishes a framework to measure the perception of these acoustical changes and investigate the extent to which people are capable of determining when they are in the location of the coupling aperture using auditory cues alone: a term here coined the auditory perceived aperture position (APAP). This paper is laid out as follows: A background section introducing coupled room acoustics and an acoustical analysis of room transitions is presented in Sec. II. The theory of the auditory perceived aperture position is explored in Sec. III. A framework for an in situ listening test to measure the position at which people determine the boundary between coupled rooms using only acoustical cues is described and conducted in Sec. IV, and the results are discussed in Sec. V, as well as considerations for how the framework could be improved upon in further iterations. The test paradigm is rendering free, avoiding any potential issues that could be introduced from the use of measurements, simulations, and auralisations. The paper is concluded in Sec. VI, along with potential applications of the findings, limitations of the study, and future work.

In a single shoebox room, the reverberant energy decay typically follows an approximately exponential decline, though, in practice, asymmetrical absorption does produce some anisotropic effects (Gover et al., 2004). The corresponding energy decay curve (EDC) can generally be characterised as a single-slope decay, and the reverberation time (RT) can be obtained from the extrapolation of the slope (Schroeder, 1965). However, when two rooms with different RTs are connected via a sufficiently small aperture, and the volumes of the rooms are large enough such that energy exchange occurs between the two spaces, the diffusion characteristics can be much more complex (Billon et al., 2006), with directional elements perceivable through to the late decay (Alary et al., 2021). The resulting EDC of a coupled space features the reverberation characteristics of both rooms and is referred to as a double-slope decay (Bradley and Wang, 2005).

Double-slope decays are perceivable and distinguishable from single-slope reverberation decays (Ermann, 2007; Luizard et al., 2015a); however, the metrics for categorising single-slope RTs, such as defined in ISO 3382 (International Organization for Standardization, 2008), are undefined for double-slope decays and are therefore not comparable. Multi-slope decays are instead typically reported as a number of RTs and their corresponding amplitudes. Reverberation quantifiers specific to coupled spaces have also been established (Bradley and Wang, 2009), such as the bending point, where the amplitude of the second decay becomes louder than the first on an EDC (Luizard and Katz, 2011, 2014), and the common slope theory, which suggests that the EDC of a coupled space can be modeled at all listener positions using the same decay times and only varying decay amplitudes (Götz et al., 2022). The main perception of reverberance is considered to be largely caused by the early decay (Atal and Schröder, 1966; Bradley and Wang, 2005) and DRR (Ellis and Zahorik, 2019, 2021). However, coupled rooms can increase perceived reverberation while retaining a high level of clarity (Poletti, 2011). This may be desirable for retaining a high speech intelligibility level, for example (Beranek, 1996).

When considering the coupling aperture between two spaces, a greater aperture size leads to a higher perceived reverberation due to the increased energy exchange between the two spaces (Bradley and Wang, 2005), and the just-noticeable-difference in coupling aperture size is reported to be approximately 10% (Luizard et al., 2015b). While the perception of coupled space reverberation has been investigated, little exists on the auditory perception of the transition between two adjoined spaces. In this study, the term coupled rooms is used to describe adjacent spaces that are connected through a physical aperture. This allows energy transfer between the two spaces and means regions may exist in which occlusion and diffraction effects occur. Double-slope energy decay curves may exist, but if the reverberation characteristics of the two rooms are similar, this may not be evident.

Previously, a dataset of spatial room impulse responses was measured for the transition between coupled room pairs (McKenzie et al., 2021a). Four source positions were measured for each room pair (two in each room) from 2.5 m inside the first room to 2.5 m inside the second. Of the two source positions in each room, one had a continuous line-of-sight (CLOS) between the source and receiver for all receiver positions, and the other had no CLOS, due to the occlusion of the direct path between the source and receiver when in opposing rooms. Analysis of the measurements showed clear trends. First, the rate of energy change is the highest around the position of the coupling aperture. This is observed for configurations both with and without CLOS, though energy change is higher for those with no CLOS. The orientation of the source has a significant effect, with sources facing the aperture producing strong reflections from opposing walls when the receiver and source are in the same room, which do not reach the receiver when it is in the opposite room.

Second, DRR decreases when the source and receiver move into opposing rooms with no CLOS, due to the lower relative amplitude of the direct sound caused by occlusion. DRR is also higher in general for less reverberant rooms, as expected. These effects are greater when the difference in reverberation between the two rooms is larger, and change depending on the source position: when there is a CLOS between the source and receiver during the room transition, for example, the change in direct-to-reverberant ratio is significantly less pronounced.

Third, directional analysis showed that the reflection patterns are generally consistent in each room, but are highly complex within the approximate 1 m region around the coupling aperture. Additionally, strong reflections are observed, sometimes with a greater amplitude than the occluded direct path, especially around the coupling aperture. The edge diffraction portalling effect commonly occurs when the source and receiver are in opposing rooms with an occluded direct sound (Billon et al., 2006; Xiang et al., 2009), though the type of door at the position of the coupling aperture, such as a sliding or rotating door, affects propagation (Luizard and Katz, 2014). Portalling is used in this paper to refer to scattering and diffraction around the coupling aperture, which produces the impression of sound source location being through the coupling aperture (Raghuvanshi and Snyder, 2018).

When moving from one room to another, the auditory changes around the coupling aperture can be abrupt. These include the loss of reflections from incoming walls around the aperture, a rise or fall in direct-to-reverberant ratio, directional changes in the dominant reflections, and depending on the source position, the potential occlusion of the direct sound (McKenzie et al., 2021a). A new term is coined in this paper. Whereas the coupling aperture refers to the physical boundary between two spaces, the APAP is herein used to refer to the physical position at which a person perceives they are at the position of the coupling aperture, when using only auditory cues. The APAP is likely inferred from a combination of auditory cues, including changes in reverberation strength (Bradley and Wang, 2005; Ellis and Zahorik, 2021), direction-of-arrival of incoming sounds (McKenzie et al., 2021a) and double-slope decays (Luizard et al., 2015b). A number of research questions are posed in this study. How closely does the perceived position of being in the boundary between two rooms, judged using auditory cues alone, compare to the physical aperture position? How much does the range of answers vary between different individuals? How is this relationship affected when using different auditory stimuli, sound source locations, and listener orientations? How robust are these observations when considering other coupled room pairs with different reverberation characteristics? How much does this perception vary between individuals? The findings of this research could be used in the design of video game engines spatial room impulse response (SRIR) interpolation algorithms and coupled space reverberation simulations in order to provide a perceptually accurate auralisation of the transition between rooms.

By listening to the reverberation of a signal, humans are in some cases able to determine the geometry of the space (Khaykin and Rafaely, 2012). People can even locate where they are in a room, though sighted people are less accurate than blind people (Després et al., 2005). Echolocation, a skill used for navigation most typically in bats and dolphins whereby noises are self-made for the purpose of location through acoustic reflections made by the space, can also be learned in humans (Kolarik et al., 2014; Thaler and Goodale, 2016). Though this has mainly been reported for partially sighted or blind humans, sighted individuals can also learn echolocation (Norman et al., 2021; Wallmeier et al., 2013). This study hypothesises that despite the limited ability and training of sighted people to locate themselves in a room using only auditory cues, due to the complex nature of the acoustics around the coupling aperture, it may be possible to determine when one is at the position of the coupling aperture using auditory cues alone.

An important part of this study is the range of answers between participants for each condition. With a view to immersive rendering, such as in game audio engines and dynamic binaural auralisations, a simple switch between room reverberation characteristics when transitioning from one room to another would likely be insufficient as the change would be too abrupt. The change from one room's reverberation to its neighbour will be perceived over a region of space, where the expectation would be that adjacent rooms with bigger differences in reverberation would have a smaller range in answers to adjacent rooms with more similar reverberation characteristics.

Other secondary factors in judging the APAP could include differences in ambient noise between the rooms, such as air conditioning units, windows, and wall thickness. Echolocation of self-made noises such as footsteps and speech can aid perception of location (Kolarik et al., 2014), which may also help determine the APAP. Non-acoustical cues such as an imbalance in temperature and light between the two rooms may also have an effect, as could proprioception and kinaesthesia.

To assess the position at which listeners perceive the boundary between adjoined rooms using auditory cues alone, a listening test was conducted in situ using two room pairs situated in the Acoustics Lab at Aalto University, Finland. The decision was made to perform the test in situ and rendering free, rather than to use auralisations, in order to avoid any potential issues that could arise due to inaccurate geometrical acoustics modelling software or measurement and reproduction, and to focus on a natural and non-lab environment.

The two room transitions investigated in this paper are a storage room to a stairwell and a kitchen to an office; the geometries of which are illustrated in Fig. 1. The volumes, reverberation times (RT60), and background noise levels of the rooms used are presented in Table I, where RT60 is estimated from impulse response measurements taken at a distance of 2.5 m from the coupling aperture. All measurements were made with the rooms uncoupled (closed aperture), and without the carpet as shown in Fig. 3. Therefore, the measured reverberation times would have likely been lower in the experiment, due to the presence of the carpet. RT60 values are estimated as the mean of calculations at 500 Hz and 1 kHz frequency bands, extrapolated from a T30 curve fitted from –5 to –35 dB. Background noise level was measured using a Sinus Tango sound pressure level (SPL) meter, again at a distance of 2.5 m from the coupling aperture.

EDCs with two fitted linear slopes of the tested room transitions, obtained from measurements in McKenzie et al. (2021a) with the source inside the less reverberant room and receiver at the position of the coupling aperture, are presented in Fig. 2. These demonstrate the double-slope behaviour of the Storage to Stairwell transition, and the closer to single-slope behaviour of the Kitchen to Office transition at the position of the aperture.

A summary of the eight listening test conditions is presented in Table II. For the four loudspeakers playing separately (C1–C4), a dry recording of a drumkit was used as the stimulus. Preliminary studies used both drums and speech but no significant differences were found, which supports the findings of the listening test in Luizard et al. (2015b). The locations of the loudspeakers are illustrated in Fig. 1. The loudspeakers used were Genelec 8331 A coaxial loudspeakers, with the centre of the drivers at a height of 1.5 m, corresponding to an approximate average height of the human mouth (Roser et al., 2013), and driven at an root-mean-square (rms) level of around 70 dB. In each room, there was one loudspeaker with and one without CLOS to the listener for all positions, whereby those without CLOS would be partially occluded at some point during the transition.

For the Self-Noise condition (C5), participants were instructed to clap, click, speak or whistle in whichever way they felt appropriate to excite the space as they moved through the transition. This is the closest condition to emulating some effect of echolocation, which has been shown to be used along with self-motion to obtain one's orientation (Norman et al., 2021; Wallmeier and Wiegrebe, 2014).

The next condition (C6) was a synthesised cocktail party, whereby all four loudspeakers played simultaneously. Each played back a different 17 s repeating excerpt of four simultaneous anechoic speech recordings, consisting of two male and two female speakers, resulting in a total of 16 speakers at one time. In addition to the speech, low level white noise was also included at an approximate rms level of 15 dB lower than the speech, in order to reduce the effect of reverberation and to mask ambient background noises that may have been present in the coupled rooms during the experiment. Contrarily, an Ambient condition (C7) was included in which there was no active auditory stimulus, only background noise.

In the final condition (C8), participants wore Bose QuietComfort 35 II wireless headphones, with the active noise cancellation (ANC) turned to full. The headphones played back continuous pink noise at a level of approximately 70 dBA. This condition was chosen to remove any auditory stimulus completely and was intended as an anchor.

For controlled movement between the rooms, participants sat on an office chair mounted on a pallet jack, as shown in Fig. 3, and were pushed forward and backward by a researcher. In a pilot study, participants had been able to walk along the transition path whilst holding onto a handrail for balance, but this was thought to give non-auditory cues on the speed and range of movement, thus allowing participants to identify the APAP based on proprioception and kinaesthesia alone. The office chair was deemed more disorientating, as participants could often not tell the direction in which they were moving. The researcher wore socks to quieten his footsteps and moved at a consistent speed for all participants. Participants used hand signals to gesture whether to move forward, backward, stop, and to indicate when they felt they were in the position of the coupling aperture.

To ensure the path of the pallet jack was smooth, and to remove potential auditory cues from the floor, two floorboards of 3 m length were placed in the path between the two rooms, with a 0.4 m offset between the crossover between the floorboards and the coupling aperture. The floorboards were raised above the door frames and clamped together. An 8 m long carpet was placed on top of the floorboards which made the movement of the chair quieter. The SPL when pushing the pallet jack across the carpet at walking pace was measured using a Sinus Tango SPL meter at an approximate sitting head height as 38 dBA, which is comparable to the background noise levels of the rooms used in the test (see again Table I). This may have had some effect on the experiment, as the movement of the pallet jack will have been an audible, albeit quiet, noise source present for all conditions. A piece of tape was laid on the carpet with distance markings every 5 cm. A headrest was used to align the ears of the participants with the centre of the chair, such that when the chair rotated their ears were still in the centre, and some string was placed at the bottom centre of the chair to measure the ear position on the carpet. To further minimise the possibility of non-acoustic cues influencing APAP results, participants were blindfolded and instructed to close their eyes. The path of movement was approximately 6 m, with the midway point close to but not exactly at the point of the coupling aperture, to avoid a potential proprioceptive cue. Participants were not allowed to speak, except in the self-noise condition (C5).

Participants were instructed to face forward and not turn their heads sideways (minor movements were allowed). They faced the same orientation for the duration of a trial. Half way through the test, after eight trials, the chair turned around to face the opposite direction. An even number of participants began the test facing each direction. The ordering of test conditions was randomised before being repeated with the condition order reversed, making 16 overall conditions. The reversal of the condition order halfway through the test was to avoid potential learning bias in the results.

The procedure for a single trial was as follows. It would begin with the participant facing the aperture, at 2.5 m inside one room. The chair would move forwards toward the aperture, at a constant speed that was approximately walking pace. The participant would then signal to continue moving forward, to stop, or to move backward (though their orientation would remain the same). They could move forward and backward as much as they wanted, and when they felt they were in the position of the doorway between the two rooms, they indicated so using a thumbs up or equivalent. The researcher then measured the position of the ears using the tape on the carpet.

Fourteen participants took part in each test, though some participants took part in both. Participants were aged between 24 and 38, (12 male, 2 female in the Storage to Stairwell transition and 11 male, 3 female in the Kitchen to Office transition) with self-reported normal hearing and prior critical listening experience (such as education or employment in audio or music engineering). The results were first tested for normality using the Shapiro-Wilk test, which found some data distributions to be non-normal. Note that as the acoustical changes of room transitions are not symmetrical, the range of answers for each condition was expected to be asymmetrical as well. Statistical analysis was conducted using non-parametric methods.

For both tested room transitions, the APAP results for each condition, with different participant orientations plotted separately, are presented as violin plots in Fig. 4. Violin plots display the density trace and box plot in a single illustration (Hintze and Nelson, 1998). The width of the violin shows the density of data, median values are presented as a white point, the interquartile range (IQR) is marked using a thick gray line, the range between the lower and upper adjacent values is marked using a thin gray line, and individual results are displayed as dots. For visibility, the IQRs are also presented separately in Fig. 5.

First, as expected, the ANC Headphones condition (C8) produced APAP results that were the furthest from the physical coupling aperture position, as illustrated by the high IQR. In both tested transitions and orientations, the IQR of C8 included positions above 1 m away from the physical aperture position, which was not observed for any other condition. This confirms that participants were using auditory cues to locate the APAP and that the experimental design was sufficient to minimise proprioception and kinaesthesia. Some participants noted that this condition was almost impossible and admitted to guessing, whereas others suggested a possible change in room temperature, though they admitted that this was speculation.

The four loudspeakers (C1–C4) produced APAP results that were generally close to the physical aperture position, with the IQR falling within ±50 cm and the total range within ±1 m for 11 of the 16 tested loudspeaker positions and participant orientations. To assess whether loudspeaker position had a significant effect on APAP results, Friedman's analysis of variance (ANOVA) tests were conducted: for the Storage to Stairwell; $χ2(3)=7.29,p=0.063$⁠, and $χ2(3)=6.26,p=0.10$⁠, facing the stairwell and the storage space, respectively, and for the Kitchen to Office; $χ2(3)=20.57,p<0.01$⁠, and $χ2(3)=5.57,p=0.13$⁠, facing the office and the kitchen, respectively. Therefore, though loudspeaker position did have an effect on APAP, this was only statistically significant at a confidence interval of 95% for the Kitchen to Office transition when facing the office, which is likely due to C3 (LS 3, no CLOS, in the office), as observed in Fig. 4. Post hoc Wilcoxon signed-rank tests using the Bonferroni-Holm correction (Holm, 1979) were conducted between LS 3 and the other loudspeaker positions at this orientation and room transition, which confirmed C3 to be the outlier (p < 0.01 in all three comparisons).

The Self-Noise (C5) did not in general produce APAP results particularly close to the aperture position for the Kitchen to Office transition, but for the Storage to Stairwell when coming from the reverberant stairwell facing the drier office, results were closer with a median of 0 cm and an IQR of less than 20 cm. However, when facing the stairwell and coming from the office, APAP results were further from the aperture position.

The Cocktail Party condition (C6), which featured overlapping speech signals simultaneously from all four loudspeakers, with white noise to mask reverberation, was relatively close to the aperture position in some scenarios but with a considerable range between participants. For the Ambient condition (C7), results varied between the two tested transitions, with APAP results close to the aperture position for the Storage to Stairwell but further for the Kitchen to Office, and with a greater IQR. Some participants noted hearing birdsong outside the stairwell during this condition, which they may have found beneficial in judging the APAP.

To obtain a more general overview of the APAP results, Fig. 6 presents violin plots of C1–C5: the four loudspeakers and the Self-Noise conditions (conditions C6–C8 are excluded for including reverberation masking noise or no room excitation stimulus). The median APAP is within ±20 cm of the aperture position for both tested room transitions and listener orientations, and the IQRs all within ±52 cm. This suggests that the participants in general located the APAP within approximately 50 cm of the physical aperture position in both tested transitions, though APAPs were closer in the Storage to Stairwell transition.

Participant orientation appears to have had a notable effect on APAP results, tending towards the opposite room to the direction in which the listener was facing. To assess the statistical effect of this, Friedman's ANOVA tests were conducted for the four loudspeaker and Self-Noise conditions (C1–C5) collated, which showed statistically significant differences between orientations: $χ2(1)=9.06,p<0.01$⁠, and $χ2(1)=25.9,p<0.01$ for the Storage to Stairwell and Kitchen to Office transitions, respectively. However, though IQR did vary with orientation, no clear trends were observed.

The median APAP for all participant orientations, for the four loudspeaker and Self-Noise conditions (C1–C5), is 2.5 cm and –4.5 cm for the Storage to Stairwell and Kitchen to Office transitions, respectively. In both transitions, this is inside the more reverberant room (see again Table I). However, as this is a small distance, it is not possible to draw a general conclusion on this.

Another observation suggests that the room in which the loudspeaker was situated had an effect on the APAP. To look at this more closely, violin plots of the APAPs for the two loudspeakers in each room are presented in Fig. 7. This shows that the APAP tended to be perceived closer to, or inside, the opposing room from the loudspeaker. Friedman's ANOVA tests to determine the statistical significance of this were conducted: for the Storage to Stairwell; $χ2(1)=5.14,p=0.023$ and $χ2(1)=5.14,p=0.023$⁠, facing the stairwell and the storage space respectively, and for the Kitchen to Office; $χ2(1)=11.57,p<0.01$ and $χ2(1)=0.14,p=0.7$⁠, facing the office and the kitchen respectively. Statistical significance for three out of the four tested comparisons indicates this effect is notable, and though not significant for the Kitchen to Office when facing the kitchen, the median values suggest the effect is still weakly observed.

To assess the differences in APAP results between individual subjects, Fig. 8 presents violin plots of C1–C5: the four loudspeakers and the Self-Noise conditions for each participant, ordered by ascending IQR. It is interesting that for some participants the APAP results are consistently very close to the aperture position, whereas for others they are much less consistent, as shown by the variation in IQR and height of the violins. The median IQRs are 41 and 57, with ranges of 17–89 and 17–129, for the Storage to Stairwell and Kitchen to Office transitions, respectively, showing significant differences between individuals.

The results of the listening test show that, for the two tested room transitions, the perceived position of the aperture between two adjacent rooms using auditory cues alone was relatively close to the physical position of the aperture. This suggests that the room transition is perceivable; however, the range of results shows that this change is not simply a switch between the two rooms. The relationship between APAP and physical aperture position varied depending on many factors, including sound source position and type, reverberation level of the coupled rooms, and listener orientation. Furthermore, the APAP results of some participants were consistently closer to the physical aperture position than others.

To investigate how the APAP results compare to objective analysis of acoustical measurements of the tested room transitions, spatial room impulse responses of the Storage to Stairwell transition from McKenzie et al. (2021a) for the four loudspeaker positions (C1–C4) were rendered binaurally, as in McKenzie et al. (2019, 2018), with the soundfield rotated to same orientations tested in this study. Figure 9 displays the mean energy of the left and right channels of the binaural impulse responses, akin to the “spatial energy variation” metric used in Luizard et al. (2014). As expected, the greatest change in energy occurs around the coupling aperture (measurement position = 0 cm), with a drop in energy in the opposing room to the loudspeaker. Apart from the energy increasing at the closest point to the loudspeaker, it stays fairly constant until approximately 25 cm before the aperture (with the exception of C2, where the energy drops at around –70 cm due to occlusion from the door [see again Fig. 1(a)].

Comparing Figs. 9 and 4(a) can give an indication of the possible cause of the results. For C1 and C2, the ranges in APAP are all approximately –50 to 100 cm. In Figs. 9(a) and 9(b), –50 cm is around where the binaural energy starts to dip significantly, and 100 cm is around where the binaural energy starts to level out again. This suggests that the period of sudden change in binaural energy could be a factor used to determine the APAP. For C3 and C4, the ranges vary more, though generally the ranges are smaller than C1 and C2 and lie between approximately –50 and 25 cm. Referring to Figs. 9(c) and 9(d), the binaural energy starts to dip significantly at around 25 cm, though there is less of a sharp flattening out and more of a continued decline as the receiver moves into the storage space. Further analysis with more tested room transitions is warranted to better investigate this link.

The horizontal direction-of-arrival (DoA) of the first seven arrivals, referring to the direct sound and loudest early reflections, was estimated using a fourth-order spherical harmonic steered plane wave decomposition beamformer (Politis, 2016) of the Storage to Stairwell transition, for C3 (LS 3 in the stairwell, no CLOS) is presented in Fig. 10. Power is normalised separately for each measurement in order to illustrate the relative intensity of the dominant arrival to the others. The plot demonstrates the strong changes in the direction and relative power of arrivals around the coupling aperture, with the greatest changes in DoA and relative amplitude occurring between $−50$ and 0 cm. Referring back to Fig. 4(a), the majority of results for both orientations of C3 fall within –50 and +10 cm of the aperture. This suggests that the direction and amplitude of reflections may play a significant role in the perception of the APAP. Corresponding plots for the source positions with CLOS (McKenzie et al., 2022) show similarly consistent DoAs in each room, with a transition in the ±1 m region around the coupling aperture that changes the most within ±50 cm. As most APAP results fell within this ±1 m region, this suggests that the region of greatest changes in the direction and relative amplitude of reflections may indeed be a factor used in perception of the APAP, as well as binaural energy.

Only one response was obtained for each condition and orientation per subject. Though this was done to limit the duration of the test and to avoid possible learning effects, it does mean that intra-subject consistency could not be assessed. However, the APAP results for each participant (for conditions C1–C5) presented in Fig. 8 demonstrate the variation between participants, with some participants significantly more consistent than others. It may be possible that with training, as with echolocation (Norman et al., 2021; Wallmeier and Wiegrebe, 2014), consistency could be improved. Further testing with more participants is warranted to assess this.

For the four loudspeaker and Self-Noise conditions (C1–C5), the APAP was largely perceived to be within ±50 cm of the coupling aperture (as shown by the IQR), which supports the theory that the reverberation characteristics of two rooms are distinct and distinguishable, and the complex changes in reverberation between coupled spaces allow for auditory self-localisation of the coupling aperture. It also supports the DoA analysis in McKenzie et al. (2021a), which showed that the greatest fluctuations in the direction and intensity of direct sound and early reflections occur within approximately ±1 m of the coupling aperture.

Loudspeaker position had a statistically significant effect on the APAP, as participants generally perceived the aperture to be inside the opposing room from the loudspeaker. This is likely explained by reflections and occlusions from the doorway, as occluded reflections will reach the ears at a small distance inside the opposing room due to the wave paths. Whether or not the loudspeaker retained a continuous line-of-sight with the listener at all positions did not in general have a significant effect on results.

One result that initially appears to be an outlier is the third loudspeaker (LS 3) in the Kitchen to Office transition, when facing the office (the room in which the loudspeaker was). Here, the median result was –68 cm. This is significantly further from the coupling aperture than the APAP results of other loudspeakers, and even of the same loudspeaker with the other tested participant orientation. A likely explanation comes from referring back to Fig. 1(b), as there is a large surface almost adjacent with the door. Therefore, when the loudspeaker is facing the door and surface, there is little change in amplitude of this reflection between –50 and 0 cm from the coupling aperture, but when the loudspeaker is 1.4 m inside the office, the direct sound occlusion from the doorway only occurs at approximately 75 cm inside the kitchen. This supports the findings in Xiang et al. (2013), which showed that source and receiver positions change the properties of the energy decays.

Another disparity between results for different listener orientations is the Self-Noise condition (C5) in the Storage to Stairwell transition. When facing the storage room, APAP results were close to the physical aperture position with a low inter-subject variation (median APAP = 0 cm; IQR = 15 cm). However, for opposite orientation (facing the stairwell), APAP results were further from the aperture position with a large inter-subject variation (median APAP = –59 cm; IQR = 72 cm). This may again be explained from reference to the geometry of the rooms [see Fig. 1(a)]. The storage space includes a wall and door close to the transition, and participant self-noise may have produced strong reflections from these objects and significantly influenced judgment.

APAP results were generally closer to the coupling aperture for the Storage to Stairwell transition. Referring back to Table I and Fig. 2, this is possibly explained by the greater difference in reverberation between the two rooms, which contributes to a larger contrast around the coupling aperture (Luizard et al., 2015b), and the more prominent double-slope behaviour of the Storage to Stairwell transition. In the Kitchen to Office transition, where the reverberation levels are lower and the contrast between the two rooms is smaller, this translates to APAP results further from the physical aperture position. Therefore, it appears that APAP range and perception is different for every coupled room pair.

Participant orientation had a statistically significant effect on APAP for both tested room transitions, whereby participants' perceived location using auditory-only cues was further in front of them than their physical location, as observed in Fig. 4. This could be due to the pinnae, which reduce the high frequency amplitude of rear incident sounds (Hebrank and Wright, 1974), and is supported by the binaural energy analysis in Fig. 9, whereby the different orientations reflect a similar offset in the change in binaural energy. In future iterations of the experiment, this effect could be investigated further by including a condition in which the pinna effects are removed, such as by placing an omnidirectional microphone on the top of the head and playing the microphone feed through headphones.

The Ambient condition (C7), with only background noise, had a notably smaller interquartile range for the Storage to Stairwell transition than the Kitchen to Office. This may be due to the larger difference in ambient level between the storage space and the stairwell. Alternatively, one study suggests that the auditory detection of walls is stronger with greater levels of low-frequency ambient noise (Ashmead and Wall, 1999). Therefore, it is possible the ambient noise of the Storage to Stairwell transition may be louder at low frequencies than the Kitchen to Office transition, even though it is lower in overall level (see again Table I). Future studies to investigate this effect further would benefit from a greater variety of coupled spaces and frequency-dependent background noise measurements.

Some of the practical limitations of the experimental setup require consideration. There was no repeat of trials: only one trial of each condition and orientation was performed per participant. Though this was chosen to avoid learning effects and reduce the overall duration of the test, it limits the amount of intra-subject consistency that can be tested. The nature of the aperture itself will have had an effect, such as the openness of the door (Luizard and Katz, 2014). In this study, the door was opened as far as possible, flush against a wall in both room pairs and approximately perpendicular. It will have produced early reflections at a close proximity, which may have been a cue used by listeners. That the starting position was consistent for all trials means that a random “chance” result would still be expected to have a median APAP around 0. Conducting future iterations of the experiment in larger rooms would allow for a longer walkway and a varied starting position. Nevertheless, the results of conditions C1 to C5 are significantly different to those of C8, which suggests the experimental setup was sufficient to draw some conclusions. Future iterations of the experiment should also investigate the potential interactions among the different experimental factors, such as between the conditions, room transitions under test and listener orientation.

This paper has introduced the APAP: the perceived position of being in the boundary between two acoustically adjoined spaces using auditory cues alone. Analysis of SRIR measurements of room transitions highlighted the complex acoustical nature of coupled rooms, especially around the coupling aperture. A framework for a listening test to measure this has been described and carried out to assess how blindfolded participants locate the APAP using only auditory stimuli, through a moving chair system for controlled transitions between coupled rooms.

Collating results from the conditions using single loudspeaker stimuli and self-noise, whereby the participant would clap or speak to excite the space, the interquartile ranges of APAP results were generally within 1 m of the physical position of the aperture. This suggests that the auditory perception of the transition point between the two rooms is relatively close to the physical aperture position in the tested room pairs. The range of results for each condition suggests that the acoustical changes when transitioning from one room to another occur over a short distance. Comparing the results to objective analysis of room transition measurements, including binaural energy and direction-of-arrival analysis, suggests that the APAP tends to be perceived within the period of greatest acoustical change. Therefore, the transition between rooms requires significant attention in plausible room acoustics rendering and modelling development. The effect is robust but varies for different stimuli, source positions, and numbers of sources. It must be noted, however, that this preliminary study was conducted with only 14 participants and two room transitions, with only one trial per condition. This limits the scope of the conclusions that can be drawn, and the test should be repeated at a larger scale in order to draw more definitive conclusions.

Various acoustical factors seem to influence the APAP, including sound source position, room reverberation amount, contrast in reverberation between the two rooms, the type of stimulus used to excite the space, and listener orientation. That these influencing factors have statistically significant effects on the auditory perceived position of the aperture means that the acoustics of room transitions are not trivial. For example, video game engines, SRIR interpolation algorithms, and coupled space reverberation simulation methods may need to take into account room reverberation amount, sound source location, and even listener orientation in order to provide a perceptually accurate auralisation of the transition between rooms. Switching between the reverberation characteristics of the two rooms at the point of the aperture is insufficient; for example, scenarios that produce a greater range in APAP results may therefore require a more gradual fade between the two rooms, and vice versa. Future work into the reproduction of room transitions should investigate plausible ways to interpolate between the reverberation characteristics of adjoined rooms.

Although this study has shown that the APAP is a perceivable auditory event, it did not establish the acoustical features of room transitions which are the most perceptually important when judging the APAP. The objective analysis suggested that both overall energy levels and the direction and relative levels of reflections may play significant roles in the perception, with the APAP within the region of greatest change. Future experiments will investigate these relationships further and for more room pairs and look to isolate the different acoustical changes when transitioning between two rooms, such as those in binaural energy, direct-to-reverberant ratio, and the direction of arrivals, as well as coupled-room features like bending point, to better understand the hierarchy of perceptual cues.

This research was supported by the Human Optimised XR (HumOR) Project. The authors appreciate the contribution of Aleksi Öyry in the listening test design.