Proceedings of the Institute of Acoustics

Acoustic effects of long-delayed reflections from rear walls in a shoebox hall

T. Hanyu, Dept. of Architecture and Living Design, Nihon University, Japan
A. Kawai, Graduate School of Science and Technology, Nihon University, Japan
R. Suzuki, Dept. of Architecture and Living Design, Nihon University, Japan
K. Hoshi, Dept. of Architecture and Living Design, Nihon University, Japan

1 INTRODUCTION

Spatial impressions are important factors for acoustic design of concert halls. Spatial impressions are divided into at least two elementary sensations such as the apparent source width (ASW) and listener envelopment (LEV)^1,2,3. Early lateral reflections within 80 ms contribute to ASW^4,5,6 and late arriving lateral reflections after 80 ms contribute to LEV^2,3. Shoebox halls are relatively easy to get strong lateral reflections thanks to narrow width between parallel sidewalls^5-9. This is considered to characterize acoustics in the shoebox halls. However, shoebox halls with parallel sidewalls do not always ensure good acoustics. Hence, hidden factors other than the parallel sidewalls may exist to create good acoustics. In shoebox halls with excellent acoustics, such as the Musikvereinssaal in Vienna, the Concertgebouw in Amsterdam and the Symphony Hall in Boston, most part of the rear walls are reflective surfaces. In these halls, reflections from the rear walls should arrive with long delays to listeners.

Ueno has studied the stage acoustics in concert halls and implied that the players on the stage prefer the long path reflection with suitable time-delays^10,11. However, as for the listeners, it is generally considered that the long path reflection causes echo disturbance. It has not been clear whether the listeners also prefer such the long-path reflections. Therefore, in this study, subjective experiments were conducted to investigate the effect of long-delayed reflections from the rear walls to the listeners.

2 EXPERIMENTAL METHOD

A dissimilarity experiment was conducted in an anechoic chamber using five loudspeakers shown in Figure 1. Six sound fields were used for the experiments. Each sound field A, B, and C consisted of a direct sound, two early reflected sounds and four reverberations as shown in Figures 2. Each of other three sound fields D, E, and F consisted of a direct sound, two early reflected sounds, two long-delayed reflected sounds and four reverberations as shown in Figures 3. The direct sound was radiated through a loudspeaker C. Two early reflected sounds were radiated through loudspeakers FL and FR. Four reverberations were radiated through loudspeakers FL, FR, BL and BR. Four reverberations were uncorrelated each other. Two long-delayed reflected sounds were radiated through loudspeakers BL and BR.

Table 1 shows playback levels of early reflected sounds, reverberations and long-delayed reflected sounds relative to the direct sound. Playback levels of the direct sound and the early reflected sounds in all the sound fields were kept constant. Major differences between the six sound fields were ΔL₁ and ΔL₂. ΔL₁ of the sound fields B and C were decreased by 6 and 12 dB respectively relative to that of sound field A. Same relationships were set between the sound fields D, E, and F. Each of the sound field D, E, and F was addition of the long-delayed reflected sounds and the sound field A, B, and C, respectively. Relative playback level of the long-delayed reflected sounds ΔL₂ was changed as shown in Table 1. Music signal used in the experiment was 20 seconds long of the beginning of Mozart's composition "String Quartet No. 14 in G major (K 387) 1st movement". Finally, A-weighted playback levels of each sound field from A to F were 63.8, 62.6, 61.8, 62.9, 64.1 and 62.9 dB (slow peak), respectively.

Table 2 shows room acoustic indexes of the six sound fields. LFC is early lateral energy fraction and L_J is Late lateral sound level. They are defined as objective measures for ASW and LEV respectively in ISO 3383-1:2009¹². All sound fields have a reverberation time of 2.2 seconds. LFC was 0.34 in all the sound fields. C80 and L_J differed depending on ΔL₁ and ΔL₂ of each sound field.

Subjects were 14 individuals aged 19-46 with normal hearing. The subjects were asked to sit in a chair in the anechoic chamber with correct posture, and were instructed to always face the direction of the front speaker. Subjects were presented with all the permutations of six sound fields, namely 30 stimulus pairs (6 × 5 = 30 pairs), and evaluated the dissimilarity of each stimulus pair on a 7- point scale from completely different to completely the same. As a result, a total of 30 × 4 = 420 responses were obtained. The responses obtained were analyzed according to Sammon's multidimensional scaling method¹³. Five patterns were prepared by randomly changing the presentation order of the stimulus pairs, and the patterns were changed for each subject.

Figure 1: Arrangement of loudspeakers

Figure 2: Structure of the impulse responses of sound fields A, B and C

Figure 3: Structure of the impulse responses of sound fields D, E and F

Table 1: Playback levels of early reflected sounds, reverberations and long-delayed reflected sounds relative to the direct sound

Table 2: Room acoustic indexes of the six sound fields

3 RESULTS AND DISCUSSIONS

There were five subjects who answered that the degree of dissimilarity for the sound field pair was 6 or more even though the sound field pairs were the same. All responses from such subjects were excluded from analysis. As a result, nine subjects were used for analysis. In addition, the stress value for the six sound field arrangements was 2.72×10^-14 for a two-dimensional arrangement, which was extremely close to 0. Therefore, we decided that the two-dimensional arrangement would be appropriate for the arrangement of the six sound fields.

Figure 4 shows the two-dimensional arrangement of the six sound fields obtained from the dissimilarity experiment. Furthermore, Figure 5 shows the relationship between the dimension 1 (horizontal axis) in Figure 5 and L_J, and Figure 6 shows the relationship between dimension 2 (vertical axis) and L_J.

First, looking at the dimension 1 in Figure 4, the dimensions are arranged as D, A, E, B, F, and C in descending order of value. This is almost the same order as L_J. Looking at Figure 5, the correlation coefficient between dimension 1 and L_J is 0.974, indicating a strong correlation. From this, it can be considered that the dimension 1 represents the degree of LEV.

Next, consider dimension 2 in Figure 4 When comparing a pair of sound fields such as sound fields A and D, which have the same level of late reverberation sound but differ in the presence or absence of the long-delayed reflected sounds, their arrangement is generally far apart in the direction of the dimension 2 (vertical axis) rather than the dimension 1. A similar tendency can be seen between sound fields B and E. However, between the sound fields C and F, the opposite trend was observed. This is thought to be due to the low level of long-delayed reflected sounds in the sound field F. These results suggest that the subjects perceived the difference in auditory impression caused by the presence or absence of the long-delayed reflected sounds. Furthermore, based on the introspection reports of the subjects, there were no subjects who perceived echo disturbance.

Looking at Figure 6, since the correlation coefficient between the scale value of each sound field in the dimension 2 and L_J was 0.073, both can be regarded as uncorrelated. The correlation between scale values in the dimension 2 and C80 was similarly low (r=0.232). This suggests that the dimension 2 is an axis that expresses an axis that expresses an auditory sensation other than LEV., which cannot be explained by L_J or C80. In addition, since the LFC, which is an evaluation index of ASW, is the same in all sound fields, it can be also said that the dimension 2 is an acoustic effect different from that of ASW. The above results indicate that the long-delayed reflected sounds may produce different acoustic effects from ASW and LEV.

Figure 4: Two-dimensional arrangement of the six sound fields obtained from the dissimilarity experiment

Figure 5: Relationship between the dimension 1 (horizontal axis) in Figure 5 and L_J

Figure 6: Relationship between the dimension 2 (vertical axis) in Figure 5 and L_J

4 CONCLUSIONS

In this study, the effect of long-delayed reflections was investigated by subjective experiments. As a result, the long-delayed reflections from the rear walls can produce an acoustic auditory sensation other than ASW and LEV. And it was also clarified that it is possible to avoid the echo disturbance due to long-delayed reflections, even if the rear walls are reflective. Reflective rear wall would be a viable option for the acoustic design of shoebox halls.

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