Influence of wall scattering on the early fine structures of measured room impulse responses.

Influence of wall scattering on the early fine structures of measured room impulse responses Jin Yong Jeon,a) Hyung Suk Jang, and Yong Hee Kim Department of Architectural Engineering, Hanyang University, Seoul 133-791, Korea

€nder Michael Vorla Institute of Technical Acoustics, RWTH Aachen University, D-52056 Aachen, Germany

(Received 10 October 2013; revised 21 June 2014; accepted 26 January 2015) The effects of wall diffusing elements on sound-field diffuseness were investigated in a tenth-scale model hall and in a real recital hall. Acoustical measurements were carried out in both halls to measure the surface diffusivity of the lateral walls. In the scale model, the surfaces of the lateral walls and the soffits were covered with diffusers; in the recital hall, the front halves of both lateral walls were treated using reflective panels and absorptive materials. Objective characteristics were investigated using conventional room acoustic parameters and the number of peaks (Np) computed for the measured impulse responses, which were recorded under diffusive, reflective, and absorptive conditions. In addition, as a measure of the diffuse sound fields, the relative standard deviations (RSDs) of the acoustical parameters were investigated. The diffusive surfaces caused a decrease in the standard deviation of the early decay time and an increase in the Np at higher frequency bands. Auditory experiments using a paired comparison method revealed that the perception of subjective diffuseness could be quantified by using Np. In addition, one listener group’s preference was correlated with Np and varied depending on different wall surface treatments. C 2015 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4913773] V [LMW]

Pages: 1108–1116

I. INTRODUCTION

Sound diffusing elements are considered one of the most critical aspects in the acoustic design of concert halls. Diffusers are used to scatter incident sound energy in order to reduce tone coloration and echo problems at the cost of a slight decline in sound strength. Determining the appropriate diffuser location and shape is an important process in acoustic design. Lateral walls have been used in concert halls as a prominent element in diffuser design to achieve diffuse reflections (Schroeder, 1979; Cox, 1995; Barron, 2009). Irregular shapes and ornamental objects in the existing 19th-century shoebox shaped concert halls were important for scattering sounds throughout the inner spaces (Bradley, 1991). On the other hand, in modern concert halls, the use of periodically repeating patterns on the interior surfaces for diffusion has been proposed (Cox and D’Antonio, 2004). For the practical design of concert halls, surface designs that reflect conceptual diffusion profiles are often considered without regard for the quantitative measurements specified by ISO 17497-1 (2004) and ISO 17497-2 (2012). The scattering coefficient is the scattered energy portion of the total energy and is calculated from the specular reflected portion, whereas the diffusion coefficient is used to describe the uniformity of directional scattering distribution based on surface diffusivity (Cox and D’Antonio, 2004; Cox et al., 2006). Recently, investigations have been conducted on the perception of spatial differences caused by the degree of surface corrugation on lateral walls (Ryu and Jeon, 2008; Jeon a)

Author to whom correspondence should be addressed. Electronic mail: [email protected]

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J. Acoust. Soc. Am. 137 (3), March 2015

et al., 2012). Scale models of diffusers of various shapes were measured to establish the material characteristics for each basic shape (Chiles and Barron, 2004; Jeon et al., 2004; Kim et al., 2011a). From these studies, the acoustical parameters for sound-field diffuseness were determined (Kim et al., 2011b); however, the quantitative sound diffusion aspect still needs to be investigated. Davy et al. (1979) suggested that the standard deviation of reverberation time (RT) could be used as an indicator in the evaluation of diffuse sound fields. There have been several attempts to measure the spatial changes in a sound field due to variations in diffusivity inside an enclosure (Hanyu, 2010). The relationship between perceived diffuseness and acoustic parameters of a hall was determined by Ando and his colleagues (Ando, 1986; Singh et al., 1994). Ryu and Jeon (2008) found that acoustical parameters, such as sound pressure level (SPL) and early decay time (EDT), affect the subjective preference of auralized sounds. However, there is little adequate measure for quantifying sound diffusion in temporal fine structures. The impulse response (IR) is a set of reflections, including direct sound and reverberation (Kuttruff, 2009). Therefore, reflection scattering by wall diffusers should result in measurable IRs. Recently, diffuse field parameters have been proposed based on analysis of the IRs in a space (Jeong et al., 2010, 2013; Jeong et al., 2012; Hanyu, 2013). Jeong et al. (2010) suggested methods to determine transition time to detect the strong peaks in IRs. Jeong et al. (2012) and Jeong et al. (2013) have proposed the slope ratio in the Schroeder decay curve as a means of detecting acoustic defects, such as strong reflections. Hanyu (2013) also evaluated the sound-field diffuseness to measure the time

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variation in reflected sound energy in the IRs, using a Schroeder curve. These previous studies were based on the decay curves to obtain a rough estimation of the IRs. In this study, however, the reflections from each of the spatial and temporal fine structures of the room IRs will be embedded in each IR because of wall scattering effects. The term “diffuseness” is actually interpreted in several ways. One interpretation considers the basic assumption of an isotropic sound incidence at a certain receiver point. The theoretical consequence is that the sound energy in a closed space is distributed uniformly and with equal probability. In a similar way, the reverberation is going to be uniform in the whole space. The temporal domain is the focus of this investigation, i.e., the linearity and smoothness of the Schroeder curves in the IRs. When the decay is smooth and when the decay in the dB level of the IRs is linear, the sound is more reverberant with a certain diffusion level, which is why reflections come from all possible directions and cause the IRs to decay smoothly. In this paper, sound field variations by wall scattering in concert halls are characterized to understand the acoustic behavior of diffusers objectively and subjectively. For this purpose, some objective parameters are proposed to describe the change in sound fields according to the diffusive designs in concert halls and its relationship to conventional room acoustical parameters. Two different music performance spaces (a scale model and a real recital hall) are selected as measurement venues with consideration of the variation in size and acoustical conditions. Both halls have different surface treatments (lateral wall conditions close to the stage). The IRs in different seats are measured and convolved with music signals for preference tests. Auditory test results confirm the effectiveness of the proposed objective parameters.

B. Number of peaks 1. Background

II. METHODS

In geometrical room acoustics, IRs are modeled based on the sound source and listener positions. Acoustic waves can be approximated as rays with defined amplitude and time delays (Kuttruff, 2009). The first ray that arrives without any interference is the direct sound. The other rays are reflections that decay with an exponential envelope caused by surface absorption and inverse square law attenuation. The early arriving reflections are characterized by the room shape and the specific sound paths. A physical reflection corresponds to a bundle of rays generated by the hall’s surfaces, including stage enclosures, floors, walls, or ceilings. Reflections from rough surfaces decrease the peak reflection levels, and increase the reflection density in the time domain (Vorl€ander, 2008). In this way, an IR signal that is uniformly reflected from a rough surface shows smooth decay in its structure. The parts of the IR with rapid changes in intensity represent the points where its smooth decay changes. These changes in the signal are considered as defects in its structure and a deviation from the global regularity (Ristic et al., 2014). In the Np analysis, the appearance of early reflections can be treated as those points in the IR signal where the defects in its structure appear. There are remarkable sudden changes in signal intensity and its regularity in these locations. It is clear that high Np values indicate points where the signal changes, so it was assumed that these high Np values indicate the presence of reflections in the IR. By examining the room impulse reflections, it should be possible to gauge the amount of diffusion by characterizing temporal structures by counting peaks in IRs. The fundamental idea behind this concept is that specular reflections are compact in their time domain response, whereas scattered sound is distributed over an extended temporal response.

A. Spatial distribution

2. Counting number of peaks

Davy et al. (1979) used a reverberant chamber and predicted standard deviations of RT to define the diffuse sound field by comparing the measurement results to theoretical predictions. When the experimental value is lower than the theoretical value, the space is considered diffuse. However, the deviation of RT in a small space and the spatial variance among different halls according to the condition of diffuseness has not been reported. Therefore, in order to assess the effect of diffusers on the variation in early reverberation of different spaces, the relative standard deviations (RSD) for EDT (RSDEDT) were investigated. RSDEDT is defined as the standard deviation of the EDT divided by its mean in the space. The degree of diffuseness was then evaluated for other acoustical parameters (Jeon et al., 2012). The RSDs of G, 1-IACCE3, and number of peaks (Np) were also considered, but the RSD of C80 cannot be calculated because the C80 varied from minus to plus values. For the variation of C80, the standard deviation was calculated. The RSD values can evaluate the spatial distribution of the acoustical parameters to indicate the homogenous of sound field in a concert hall.

Room IRs were acquired by measuring the direct sounds and reflections between the source and the receivers. The shapes of the local maxima are merged in the IR. They vary with the spatial features, shapes, surface absorptive characteristics of the spaces, and the band filters used in the instrumentation. Considering the difference in reflections in the temporal domain of the IR, the degree of sound diffusion can be defined as the number of peaks (Np) within the lapsed time of the effective amplitude drop. This concept has general relevance to the Schroeder frequency; it gives the transition of individual peaks to a region of peak overlap. Peaks that are local maxima in the IR are not reflections, but are arbitrary maxima in overlapping reflection components. When filtering is applied, Dirac pulses form a specific waveform: the octave filtered IR. This response involves an onset, two/three maxima, and then an offset. When room reflections meet at similar delay times, the IR has some peaks at which the maxima coincide, resulting in cancellation when the two intersecting peaks have opposing phases. A simplified but useful model for human perception suggests that audibility is dependent on the resultant waveform on a dB

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scale rather than the phase itself. Consequently, the number of peaks represents the degree of sound-field diffuseness. 3. Cut-off level

A cut-off level must be defined in order to consider the effective peaks to be audible reflections that contribute to spatial impression. In 1971, Barron investigated the threshold of a single-sided reflection for spatial impression and found it to be between 25 and 20 dB (Barron, 1971). Ten years later, Barron and Marshall (1981) used indirect investigations from previous studies (Reichardt and Schmidt, 1966, 1967) to determine a threshold of 14 dB for lateral reflections relative to direct sound to be a limen for spatial impression. Therefore, a sound level difference of 20 dB between direct sound and the resulting reflections can be determined to be within the audible range of the listener. This means that a 20 dB range is the range that can be used to identify a running reverberation of music during a symphony. In this study, a 20 dB cut-off level was used as the initial calculation of number of effective peaks, as shown in Fig. 1. Although there may be a large variance in the number of peaks, a fixed criterion is required to verify the effectiveness of this comparative parameter. A comparison with different cut-off levels (10, 20, 30 dB) is discussed in Sec. III with the respective Np values measured in the halls.

FIG. 2. Floor plan with source and receiver positions (Hall A). The dotted lines indicate the locations of the lateral wall diffusers.

The IRs were binaurally measured at 15 audience positions in the stalls. A high-voltage spark source located at the soloist position on the stage was used to create an impulse. A miniature dummy head containing two 1/8 in. microphones was used as a receiver. It was placed facing the sound source. The sampling rate of the IRs was 192 kHz in the tenth-scale model. When applying the Np, both the left channel (the microphone closest to the lateral wall) signals and the right channel signals were calculated from the measured binaural IR. In this study, Np values from the two channels are averaged to form a single value to describe the diffuseness in the left and right directivities with related to the human perception. B. Hall B

III. MEASUREMENT AND RESULTS A. Hall A

The 1400-seat Gimhae Arts Hall (Hall A) located in Gimhae, South Korea was designed with a proscenium arch and an orchestra shell. As shown in Fig. 2, diffusers were installed on the hard and flat lateral wall surfaces in order to investigate irregular reflections in the tenth-scale model hall. As described in Ryu and Jeon (2008) and Jeon et al. (2009), polygon-type diffusers with trapezoidal grating were installed on the lateral walls of the stalls. Hemisphere diffusers were also installed on the proscenium walls and sidebalcony soffits. The scattering coefficients (ISO 17497-1, 2004) of the two types of diffusers were 0.9 and 0.6, respectively, between 500 and 3.15 kHz. The scattering values were determined when the average structural length was larger than the wavelength of the effective frequency (also refer to the annex of Vorl€ander, 2008).

FIG. 1. Example of the effective peaks for the measured IRs within 20 dB from the maximum amplitude marked as solid circles (black: with diffuser; gray: without diffuser) at the same receiver position with and without diffusers. The IRs were measured in a 1/50 scaled model hall (Kim et al., 2011b). 1110


The 433-seat Sejong Chamber Hall (Hall B) located in Seoul, South Korea is described by Jeon et al. (2012). As shown in Fig. 3(a), it uses reverse-fan shaped and tilted lateral walls designed with saw-tooth-type diffusers (onedimensional corrugations) to provide diffusive reflections. Both the structural length and depth of the diffusers vary from 0.3 to 1.2 m. The diffusers were made from

FIG. 3. (a) Floor plan with source and receiver positions (Hall B). The dotted lines indicate the locations of the reflective or absorptive materials and (b) the treated lateral walls. Jeon et al.: Influence of wall scattering on diffuseness


FIG. 4. Np distribution according to the source-receiver distance in different cut-off level (10 dB, 20 dB, and 30 dB) related to direct sound.

60-mm-thick glass fiber-reinforced concrete. The tenth-scale model of this profile provided a scattering coefficient of 0.52 between 500 and 3.15 kHz. To achieve the diffusive, reflective, and absorptive sound fields, 5 mm plastic boards and/or 8 mm microfiber fabrics were installed on the lateral walls in the real recital hall. The average absorption coefficient of the plastic board was 0.08. The fabric seat on the board with a 100 mm air-gap underneath showed an absorption coefficient of 0.68. As shown in Fig. 3(b), the area of the reflective or absorptive materials was 77.8 m2, which covered two thirds of the audience lateral wall surfaces. C. Results

As shown in Fig. 4, the 20 dB cut-off level was compared with the cut-off level of 10 and 30 dB in Hall B, and with the uncertainty of Np. The Np values at the 10 dB cut-off level were ⱗ 100 peaks in all the measured positions, with the result that the limits of discrimination and the counted peaks were varied by repeated measurement in the same position. The Np values with the cut-off level of 30 dB can be used; however, the values are normally higher in all positions that have less discrimination, especially in the rear seats, than those of cut-off level 20 dB.

The Np analysis was carried out for the room IRs measured in Hall A and Hall B. Figure 5 shows the absolute values of Np within the first 80 ms after measuring the IRs at specific positions according to the absence and presence of diffusers. Figure 5 indicates that the Np values generally increased when diffusers were present. In addition, the Np values are increased by increasing the source to receiver distance. When the receiver is close to a source, the number of diffuse reflections is smaller than the values in the rear positions where the direct sound level is low. This means that the sound-field diffuseness (perceptual) at the rear seats in a hall is mainly affected by reflections from all of the surfaces in the hall, rather than some diffusing elements close to the source. Therefore, when the direct sound level is high, Np is lower in number, and for a low direct sound level, it is higher. It seems that humans cannot detect IRs below 20 dB (a relative cut-off level), which was incorporated into the calculation of Np. In this study, the authors focus on comparing the perceptual diffuseness at a certain position with the difference in Np, both with and without diffusers. Tables I and II show the conventional acoustic parameters (Ryu and Jeon, 2008; Jeon et al., 2012) and the Np parameters for Hall A and Hall B, respectively. The results of the early reflection (80 ms) show that the diffusive surfaces decreased the G and RT as a result of the weakening of the specular reflections and the smoothening of the sound decay in Hall A. With respect to C80 and 1-IACCE3, these parameters increased due to the wall scattering in Hall A. An increased C80 is a natural consequence of a decreased RT and EDT. C80 increased by 0.1 dB in Hall A, but decreased by 0.1 in Hall B. On average, 1-IACCE3 increased by 0.01 in Hall A, but no significant changes for the average of 1-IACCE3 were observed in Hall B. In Hall A, it was possible to switch between the two conditions, diffusive and reflective, through the installation of wooden hemisphere diffusers on the wall. The diffusive condition in Hall B was the original hall condition and, in order to achieve reflective and absorptive conditions, plastic panels and absorptive sheets were artificially added in front of the diffusers, which prevented implementation of a fully reflective case (Jeon et al., 2012). This generally indicates that diffusive surfaces decreased mainly EDT for both halls as a result of the weakening of the specular reflections from the lateral walls and

FIG. 5. Np distribution according to the source-receiver distance in diffusive, reflective, (and absorptive in Hall B) conditions in (a) Hall A and (b) Hall B.



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TABLE I. Acoustic measurement results and RSD of the parameters in Hall A (Ryu and Jeon, 2008). Parameters

Diffusive

Reflective

1.12 0.09 1.00 0.23 5.2 0.04 6.42 1.11 0.67 0.18 138 0.61 33 0.90

1.17 0.07 1.05 0.28 5.7 0.07 6.35 2.10 0.66 0.29 117 0.67 21 0.88

RT (s) RSDRT EDT (s) RSDEDT G (dB) RSDG C80 (dB) Standard deviation of C80 1-IACCE3 RSD1-IACCE3 Np,Early RSDNp,Early Np,Late RSDNp,Late

the smoothing of the sound decay. However, other parameters did not show any consistent tendencies with respect to the presence of diffusers. Moreover, most changes of the averaged values are of 5% by absorbing wall reflections. Therefore, the methods where averaged values of acoustical parameters are compared are not sufficient to characterize the variation in the sound field that results from wall scattering. As for the spatial distribution and fine temporal structures, RSDs of RT, EDT, G, and 1-IACCE3, standard deviation of C80 were additionally calculated, including the averaged Np values (Np,Early: 0–80 ms; Np,Late: 80–200 ms) as shown in Tables I and II. In Hall A, the diffusive cases showed a lower RSD and standard deviations for all acoustic parameters than the reflective cases did. The RSDs of RT, EDT, and G decreased by 2%, 5%, and 3%, respectively. The standard deviations of C80 decreased by 0.99 dB. However, in Hall B, the diffusive cases showed little change in RSDs of RT, EDT, G, and C80. Interestingly, the RSD of 1-IACCE3 and of the Np values showed similar tendencies, but different changes were observed in both halls with TABLE II. Acoustic measurement results and RSD of the parameters in Hall B.

RT (s) RSDRT EDT (s) RSDEDT G (dB) RSDG C80 (dB) Standard deviation of C80 1-IACCE3 RSD1-IACCE3 Np,Early RSDNp,Early Np,Late RSDNp,Late

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Diffusive

Reflective

Absorptive

1.18 0.02 1.11 0.03 9.04 0.16 2.9 1.16 0.64 0.19 284 0.63 225 0.94

1.18 0.02 1.12 0.03 8.63 0.14 3.0 1.20 0.64 0.15 240 0.57 137 0.89

1.00 0.02 0.99 0.05 7.91 0.21 4.4 1.44 0.54 0.22 181 0.61 56 1.08


respect to the diffusive lateral walls. The RSD of 1-IACCE3 decreased by 11% in Hall A, but increased by 4% in Hall B. Likewise, RSDNp,Early decreased by 6% in Hall A, and increased by 6% in Hall B. The change in the mean of the Np resulting from the wall scattering went from 10% to 20% of the increased effective peaks of the temporal fine structures in the IRs. The higher RSD of Np,Early in Hall A results from the rear seats having an Np that increased much higher due to the diffusive lateral walls. These tendencies have a greater contrast when considering the absorptive case of Hall B. The Np of the absorptive case was the lowest due to the lack of effective lateral reflections. The spatial distributions of the acoustical parameters are useful to examine the tendencies of the sound field, but these parameters are not the absolute values that can explain the diffuse sound field. Figures 6(a) and 7(a) show the scattering effects of the diffusers in the frequency bands of RSDEDT in Hall A and Hall B, respectively. The RSDs of EDT showed fluctuating values according to the frequency bands. The RSDs of EDT decreased by 1%–20% for the diffusive case of Hall A. Wall scattering in Hall B yielded RSDs of EDT that increased by 2%–3% at low frequency bands (125–250 Hz), but decreased by 1%–5% at high frequency bands (2–4 kHz). In comparison to the case of Hall A, consistent tendencies caused by wall scattering were found in the results of RSD of EDT. Notice that the absorptive condition has the highest of all frequency bands. Moreover, the frequency characteristics of the Np values from Hall B also showed a similar tendency with both the Np values in Hall A and the RSDs of EDT in both halls. From the above results, the scattering effect of the diffusers can be concluded to be more noticeable at frequencies >1 kHz. The frequency characteristics of Np in Hall A and Hall B have been added in Figs. 6(b) and 7(b), respectively. For both halls, higher Np values are observed in the highfrequency bands for the diffusive condition. The differences between the diffusive and reflective conditions (including absorptive condition for Hall B) were statistically significant (p < 0.05) at >2 kHz in Hall A and at >500 Hz in Hall B. The Np values in the absorptive condition were lower than the other conditions because of the attenuated reflections from the absorption materials within the hall. IV. AUDITORY EXPERIMENT A. Subjects and stimuli 1. Session 1

Thirty musicians and postgraduate acoustics students were asked to select their preferred music samples. In order to determine their preference of the scattered sound effects, three positions at different rows (R4, R8, and R12) were selected according to the lateral wall and the source-to-receiver distances. Nine auditory signals were then prepared for cases of diffusion, reflection, and absorption one the lateral walls as shown in Table III. The auditory experiment was conducted using the paired comparison method. Nine IRs were convolved with a violin motif and presented randomly to subjects through headphones (Sennheiser HD 600). Jeon et al.: Influence of wall scattering on diffuseness


FIG. 6. (a) RSD of EDTs (RDSEDT) in octave frequency bands and (b) frequency characteristics of Np from the 15 receiver positions in a 1/10 scale model of Hall A with different surface treatments.

The violin motif of stimuli was the first movement of Mendelssohn Violin Concerto in E minor, OP.64 recorded in anechoic chamber. The stimuli lasted 7 s from the beginning of the motif. The effects of diffusers are dominant in the higher frequency bands as shown in Figs. 6 and 7. This test signal was the high frequency dominant source because of the instrumental and music piece characteristics; it is easy to assess the effect of diffusion. 2. Session 2

Twenty musicians and postgraduate acoustics students participated in the second listening session to evaluate the subjective diffuseness and the subjective preference. Ten individuals from this group also participated in session 1. Each of eight auditory signals (A2, A3, B2, C2, D1, D3, E1, and E2) was selected for the diffusive and reflective conditions in Hall A, as shown in Table IV. Four sets of listening tests were prepared that asked the preferences and diffuseness of each condition (diffusive and reflective condition). The experimental equipment and the methods were the same as those from session 1. B. Results

Responses from 30 subjects were obtained for 36 pairs of the 9 stimuli. A scale value of preference was subjected to the law of comparative judgment (Thurstone’s case V;

Thurstone, 1994). Consistency tests indicated that 23 of 30 subjects had a significant (p < 0.05) ability to distinguish between various degrees of preference. The agreement test indicated there was no significant (p > 0.05) agreement among the 23 subjects. This means that the scale value cannot represent a consistent preference response. Therefore, a cluster analysis was conducted on the responses of each subject, and the opposing two groups of responses were obtained as shown in Fig. 8. One group [G1, 15 subjects, see Fig. 8(a)] tended to prefer the rear seats, and the other group [G2, 8 subjects, see Fig. 8(b)] tended to prefer frontal seats. There was significant agreement among subjects within each of the two groups. In Table V, the group one (G1) showed a relationship between the Np and preference values. The sound-field diffuseness increased with the increase in distance between source and receiver. It is obvious from Table II that the Np increases in rear positions. There is a high diffuseness at position R12 and certain acoustical parameters, such as SPL, reduce the dB level, which is why the audience may not prefer this position (Ryu and Jeon, 2008). In addition, Np and C80 were highly correlated with the subjective preference and they were statistically significant (r ¼ 0.73, r ¼ 0.70, respectively, and p < 0.05). The scale values had a negative correlation with C80 (r ¼ 0.75, p < 0.05). It was also found that sound strength was not related to subjective preferences. In session 2, the tests of agreement were significant (p < 0.05) agreement among the subjects in the two test

FIG. 7. (a) RSD of EDTs (RDSEDT) in octave frequency bands and (b) frequency characteristics of Np from the 12 receiver positions in Hall B with respect to different surface treatments.



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TABLE III. Acoustic parameters of the selected stimuli from three positions in Hall B with respect to different surface treatments. R4

R8

R12

Positions Parameters

Diffusive

Reflective

Absorptive

Diffusive

Reflective

Absorptive

Diffusive

Reflective

Absorptive

RT (sec) EDT (sec) G (dB) C80 (dB) 1-IACCE3 Np,Early Np,Late

1.19 1.07 9.3 2.6 0.73 169 27

1.21 1.15 8.5 2.8 0.66 143 19

0.99 0.95 7.5 5.0 0.41 63 1

1.19 1.08 8.2 2.4 0.66 441 458

1.18 1.12 7.8 2.3 0.64 315 175

0.99 1.03 7.0 3.3 0.54 231 77

1.21 1.12 7.3 1.5 0.76 436 385

1.18 1.07 7.9 2.2 0.71 344 167

1.03 0.99 6.9 3.3 0.64 277 103

TABLE IV. Acoustic parameters of the selected stimuli from three positions in Hall A with respect to different surface treatments. Condition

AC

A2

A3

B2

C2

D1

D3

E1

E2

Diffusive

RT EDT SPL C80 1-IACCE3 Np,Early Np,Late

1.13 0.88 76 8.3 0.56 37 3

1.19 1.02 76 7.8 0.63 79 7

1.10 1.23 72 6.3 0.64 55 8

1.12 1.11 72 5.4 0.75 119 23

1.15 0.73 71 6.5 0.73 192 64

1.10 0.82 71 6.6 0.70 199 44

1.00 0.63 68 7.3 0.81 262 72

1.01 0.73 70 5.6 0.75 256 86

Reflective

RT EDT SPL C80 1-IACCE3 Np,Early Np,Late

1.22 1.16 80 9.7 0.50 41 6

1.14 1.16 78 7.1 0.55 53 7

1.16 1.34 70 4.2 0.50 38 10

1.16 1.11 73 5.7 0.70 104 11

1.15 0.90 73 5.1 0.71 176 55

1.08 0.81 71 7.2 0.82 176 26

1.14 0.82 70 7.0 0.80 228 33

1.09 0.79 69 6.4 0.85 252 52

TABLE V. Correlation analysis between the subjective preferences of two subjective groups (SVG1 and SVG2) and the acoustic parameters in Hall B (*p < 0.05, **p < 0.01).

SVG1 SVG2

RT

EDT

G

C80

1-IACCE3

Np,Early

Np,Late

0.20 0.17

0.34 0.04

0.34 0.61

0.68* 0.39

0.57 0.22

0.83** 0.53

0.62 0.26

TABLE VI. Correlation analysis between the subjective evaluations and acoustic parameters in Hall A (*p < 0.05, **p < 0.01). Condition

Evaluation

Group

Preference

G3 G4 — G5 G6 —

Reflective Diffuseness Preference Diffusive Diffuseness

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EDT

G

0.70 0.51 0.42

0.74* 0.69 0.47

0.84* 0.82* 0.85**

0.29 0.44 0.72*

RT


C80

1-IACC

Np,Early

0.90** 0.65 0.90**

0.26 0.13 0.36

0.84** 0.74* 0.71*

0.86** 0.78* 0.70*

0.66 0.45 0.48

0.71 0.51 0.89**

0.81* 0.92** 0.39

0.73* 0.83* 0.87**

0.67 0.71* 0.95**

0.65 0.72* 0.94**

Np,Late



FIG. 8. Scale values of preference for (a) group 1 (SVG1) and (b) group 2 (SVG2) at the three receiver positions in Hall B with wall treatments.

sets about subjective diffuseness, but the other tests about the preference were not significant agreement among the subjects. Therefore, a cluster analysis was conducted on the responses of each subject, and the opposing two groups of responses were obtained as same as session 1. Table VI shows the correlation analysis results from the four test sessions. For the reflective condition (no diffuser), there were similar tendencies of perception of preference in group three (G3) and diffuseness among the subjects. The preference and diffuseness awareness of group three (G3) were correlated with Np (r ¼ 0.86, p < 0.01 and r ¼ 0.70, p < 0.05). Listeners could perceive the diffuseness and some of them preferred the diffusive sounds in the reflective hall. For the diffusive condition (with diffuser), the subjective diffuseness and the preference had different tendencies to the correlation of the acoustical parameters. The listeners could perceive the level of diffuseness as being the same as the reflective condition; however, group six (G6) preferred the clear sound rather than the diffusive sound. In other words, listeners can perceive the degree of diffuseness and Np could explain the diffuseness, and the preference depends on the personal taste of subjects. The stimuli in the diffusive session have a correlation between RT and SPL (r ¼ 0.79, p < 0.05), and 1-IACC and SPL (r ¼ 0.89, p < 0.05). In the reflective session, 1-IACC has correlated with RT and EDT (r ¼ 0.77, p < 0.05; r ¼ 0.93, p < 0.01, respectively). V. DISCUSSION AND CONCLUSIONS

In this study, the spatial and temporal variation of sound fields caused by different surface diffusion of lateral walls was characterized from the measured IRs in a scale model and a real hall. Np was proposed as a parameter, and its effectiveness was compared against that of other acoustical parameters. Sound scattered by a wall diffuser yielded higher Np values than specular sounds did. Wall treatment with diffusers and absorbers actually affected the sound-field diffuseness, resulting in a higher Np at higher frequencies. Consequently, the degree of sound diffusion in the time domain can be evaluated by counting the number of peaks. In addition, the standard deviations of the acoustic parameters were considered in order to explain spatial-distributional aspects. J. Acoust. Soc. Am., Vol. 137, No. 3, March 2015

The direct sound level has nothing to do with the surface diffusivity of the walls. However, in this paper, Np was suggested to describe the human perception of sound-field diffuseness in different positions in a space. The relationship between the direct sound level and the amount of reflections is related to the perception of diffuseness presented by Np. When the receiver is close to a source, the number of diffuse reflections is smaller than the values in the rear positions where the direct sound level is low. This means that the sound-field diffuseness at the rear seats in a hall is mainly affected by the reflections from the entire surfaces in the hall rather than some diffusing elements close to the source. Therefore, when the direct sound level is high, the Np is lower in number, and for the low direct sound level, it is higher in number. It seems that humans cannot capture the IRs below 20 dB (cut-off level), which was defined for calculation of Np. In this study, the authors focus on comparing the perceptual diffuseness in a certain position by the difference of Np, with and without diffusers. The sound field was measured in the real hall by varying the diffusion and absorption areas on the lateral walls, and the convolved music was then evaluated. Consequently, the sound sources affected by the wall diffusers were relatively more preferred. The values of 1-IACCE3 as indicated in Ryu and Jeon (2008) and Np were highly correlated. Therefore, the variation of sound fields is related to spatial characteristics and diffuse reflections. In addition, even when the relative level of the test signals increased, the two parameters correlated well with the subjective preference regardless of SPL variation. Diffusing elements in concert halls influence the early lateral reflections. The diffuser minimizes the amplitude of the specular reflections and changes the arrival times of the reflections caused by the specular surfaces. Therefore, as it is essential for orchestra or ensemble performances to absorb the partly returned early reflections, the variation in the sound field caused by sound diffusers should be considered in auditorium design. The direction of early diffusive reflections, whether it is vertical or horizontal, should be determined by measuring the diffusion coefficients with emphasis on the incident angles. The size, shape, and position of the diffusers also need to be considered using appropriately sized scale models. Jeon et al.: Influence of wall scattering on diffuseness

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People have been trying to figure out diffusion and the subjective effects of diffusion for >50 years, but very little progress has been made. It is not easy to find out correlation of sound-field diffuseness with the perceived state of diffuseness. A further study is proposed to find out the correlation between objectively calculated soundfield diffuseness through number of peaks and preferences by auditory experimentation of perceived sound diffuseness. In addition, the value of Np should incorporate uncertainty measurements for potential use as an acoustical parameter. In this study, the same measurement system was used in different halls, including the same loudspeaker, microphone, etc., to compare the diffuseness due to the variation of wall diffusivity. The characteristics of the loudspeaker used can affect the Np, mostly due to the directivity of the speakers. The uncertainties concerning the characteristics of different loudspeakers and microphones should be considered in future studies. ACKNOWLEDGMENTS

This work was supported by the Global Frontier R&D Program on funded by the National Research Foundation of Korea grant funded by the Korean Government (MSIP) (2013M3A6A3079356). This work was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013-R1A1A2062079). Ando, Y. (1986). “Nonlinear response in evaluating the subjective diffuseness of sound fields,” J. Acoust. Soc. Am. 80, 833–836. Barron, M. (1971). “The subjective effects of first reflections in concert halls—The need for lateral reflections,” J. Sound Vib. 15, 475–494. Barron, M. (2009). Auditorium Acoustics and Architectural Design (Spon, Abingdon, Oxon, UK), pp. 1–489. Barron, M., and Marshall, A. H. (1981). “Spatial impression due to early lateral reflections in concert halls: The derivation of a physical measure,” J. Sound Vib. 77, 211–232. Bradley, J. S. (1991). “A comparison of three classical concert halls,” J. Acoust. Soc. Am. 89, 1176–1192. Chiles, S., and Barron, M. (2004). “Sound level distribution and scatter in proportionate spaces,” J. Acoust. Soc. Am. 116, 1585–1595. Cox, T. J. (1995). “The optimization of profiled diffusers,” J. Acoust. Soc. Am. 97, 2928–2936. Cox, T. J., Dalenback, B.-I. L., D’Antonio, P., Embrechts, J. J., Jeon, J. Y., Mommertz, E., and Vorl€ander, M. (2006). “A tutorial on scattering and diffusion coefficients for room acoustic surfaces,” Acta Acust. Acust. 92, 1–15. Cox, T., and D’Antonio, P. (2004). Acoustic Absorbers and Diffusers: Theory (Spon, London), pp. 1–405. Davy, J., Dunn, I., and Dubout, P. (1979). “The variance of decay rates in reverberation rooms,” Acta Acust. Acust. 43, 12–25.

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