The data was analyzed using two approaches. In the first approach, referred to hereafter as amount change, the amounts of variation of objective acoustical parameters due to the addition of the diffusers to the empty room are analyzed for the different groups reported in Table 3
. In the second approach, a series of statistical tests (Kruskal–Wallis tests) were carried out to examine the significance of difference in the acoustical parameters between the groups of configurations with the intention to analyze the effects of the type and coverage of the diffusers. As a way of data reduction with the caution of not losing important data, three frequency ranges were defined: a low frequency range comprising center frequencies ranging from 250 to 500 Hz, a mid frequency range including 1 k and 2 kHz octave bands, and a high frequency range including the center frequency 4 kHz. The choice of splitting the data into these three frequency ranges was intentionally made prior to analyzing it such that no bias was introduced in the data analysis while the frequency-dependency of the results could be maintained. For each defined frequency range, the data was averaged across corresponding octave bands, thus resulting in a single value for each of the three defined (low, mid, and high) frequency ranges.
4.1. Amount Change
In this approach, the mean value of each acoustical parameter (average across microphone positions) measured in each room configuration was subtracted from this of the empty room. The resulting difference representing the amount of change of each parameter for the configurations of each group with respect to the reference is expressed in seconds for EDT and T20
, and in decibels for C50
. These amounts of change are shown in Figure 4
and Figure 5
per octave band and discussed in the following paragraphs.
From the plots in Figure 4
and Figure 5
, it can be seen that the change in the acoustical parameters with respect to the reference generally resulted in the reduction of both EDT and T20
and in the increase of both C50
. Over 34 configurations, only five resulted in an increase of EDT, two resulted in an increase of T20
, and six in a reduction of C50
, at the center frequency of 500 Hz only. The maximum amount of change across these configurations was only of 0.03 s for EDT, 0.01 s for T20
, and 0.5 dB for C50
The amounts of change in the acoustical parameters with respect to the reference were more significant in the mid and high frequency ranges than in the low frequency range. More specifically, the reduction of EDT varied from 0 to 0.17 s in the low frequency range while it varied from 0.08 to 0.78 s and from 0.48 to 0.78 s in the mid and high frequency ranges, respectively. A similar trend was observed for T20 for which the reduction fluctuated between 0 to 0.21 s in the low frequency range, from 0.19 to 0.80 s in the mid frequency range and from 0.45 to 0.80 s in the high frequency range. As for C50, it increased from 0.1 to 4.1 dB in the low frequency range, while it increased from 2.0 to 9.8 dB and from 2.1 to 6.8 dB in the mid and high frequency ranges, respectively. Similarly to C50, C80 increased from 0.4 to 4.4 dB, from 3.3 to 12.4 dB, and from 3.4 to 9.9 dB in the low, mid and high frequency ranges, respectively.
Studying the effect of the diffusers placement on the acoustical parameters is not straightforward. To consider the effect of the placement only, an introductory analysis comparing the two configurations having the maximum and minimum values of change in the acoustical parameters for each octave band in each group was made. The latter showed that the maximum change due to the placement was 0.09 s for EDT (groups 1PF at 4 kHz, 2PF at 2 kHz, 2CF and 3CF at 500 Hz), 0.17 s for T20 (group 3CF at 2 kHz), 2.1 dB for C50 (groups 1PF at 250 Hz and 3CF at 2 kHz), 2.9 dB for C80 (group 3PF at 2 kHz). This introductory analysis also suggested that the configurations with one diffuser with the greatest distance between the source and the diffuser (those named with the letters e and c) have the lowest amounts of change in the acoustical parameters. Another brief analysis focusing on configurations with three diffusers was made to investigate if differences exist on the amount change of the acoustical parameters between configurations with a clustered diffuser installation design (those named with the letters a and m) and these having a distributed diffuser installation design (configurations named with the letters k, l, n, and o). However, the results from this brief analysis did not show any clear differences between the effect of the two defined diffuser installation designs (clustered vs. distributed) on the amount change of the acoustical parameters.
Because a maximum of three diffusers only were added in the room, the effect of placement on the change of the acoustical parameters was neglected when considering the effect of the coverage or type. Considering the coverage of the diffusers, the amounts of change averaged across both pyramid and convex diffuser types were increased as the number of diffuser varied from one to three for all the four acoustical parameters and for all the three frequency ranges. In particular, as the number of diffuser increased from one to three, EDT decreased by 0.04, 0.16, and 0.19 s in the low, mid, and high frequency range, respectively. T20 decreased even more significantly than EDT with reduction values of 0.05, 0.2, and 0.27 s in the low, mid, and high frequency range, respectively. C50 and C80 were increased as the number of diffuser varied from one to three by 0.9 and 0.8 dB in the low, 3.6 and 5.3 dB in the mid, and 3.1 and 4.9 dB in the high frequency range, respectively.
Considering the type of the diffusers, the amounts of change were slightly higher for the convex type compared to the pyramidal type in all the measured acoustical parameters and at most of the center frequencies. More specifically, for EDT and T20, the differences in the amount of reduction between the two diffuser types varied from 0 s in the 500 Hz octave band to 0.05 s in the 2 kHz octave band. The amount of increase between the two diffuser types for C50 and C80 ranged from 0 dB in the 500 Hz octave band to 1.1 dB in both 2 and 4 kHz octave bands.
4.2. Statistical Analysis
A series of 60 statistical hypothesis tests were performed to examine the significance of the effect of the coverage and type of the diffusers on the measured acoustical parameters. More precisely, this statistical analysis is done to determine if significant differences exist between groups 1P, 2P, and 3P (and between 1C, 2C, and 3C similarly) to investigate the effect of coverage, and between groups 1P vs. 1C, 2P vs. 2C, and 3P vs. 3C to investigate the effect of the diffuser type. In other words, for analyzing the effect of the coverage and excluding the effect of the type, the data points for the configurations with pyramid diffusers were grouped separately from the ones for the configurations including convex diffusers. As a result, two tests per frequency range were performed for each acoustical parameter, resulting in an aggregate of 24 statistical tests. Alternatively, in order to analyze the effect of the type of the diffusers, the data points were grouped such that the configurations with one, two, and three diffusers were separately studied to exclude the effect of coverage, thus resulting in three groups to analyze. For each of these groups, one test per frequency range was performed for each of the four acoustical parameters, resulting in a total of 36 statistical tests.
For each of the aforementioned 60 tests, the data points were examined for the conformity with the assumptions of the analysis of variance (ANOVA), namely the normality of the residuals and homogeneity of the variance, to be able to confirm if ANOVA is a suitable candidate for the purpose of the presented statistical analysis. The Shapiro–Wilk and Levene tests [23
] were performed to verify if the former and the latter assumptions were met, respectively. The results demonstrated that among the 60 tests, 35 (58.33%) were not complying with the normality assumption. As for the homogeneity assumption, this percentage was 21.66%. Consequently, the Kruskal–Wallis test was selected as an appropriate substitute to the ANOVA test. The results of the Kruskal–Wallis tests are reported in Table 5
and Table 6
for the analysis of the coverage and the type of the diffusers, respectively.
The results for the analysis of the coverage of the diffusers showed that for EDT, significant differences were observed between the configurations of all the groups in all the frequency ranges except for the group containing pyramid diffusers in the low frequency range. A same analysis for T20, C50, and C80 confirmed the existence of significant differences between all the groups only in the mid and high frequency ranges. In other words, these results indicated that increasing the number of either pyramid or convex diffusers from one to two or three had significant effect on the values of all the four acoustical parameters of the study in the mid and high frequency ranges.
The results for the analysis of the type of the diffusers indicated that the values of EDT for the configurations with one, two, and three pyramid diffusers were significantly different from the values for the corresponding convex-contained configurations only in the high frequency range. The same analysis for the values of T20 showed a significant difference only for the configurations with three diffusers and only in the high frequency range. For C50 and C80, significant differences were observed only between the configurations with two and three pyramid diffusers and their corresponding convex-contained configurations and only in the high frequency range.
Although the statistical analysis revealed that the change of the acoustical parameters with respect to the type of diffuser (pyramid or convex) is significant in the high frequency range for all acoustical parameters, the number of diffusers also seem to play a role since the significance is mainly achieved for groups containing more than one diffuser. Moreover, the differences observed in the change of the acoustical parameters due to the change of the diffuser type cannot be fully conclusive since their respective absorption area differs by 0.1 m for a single diffuser added to the room and by 0.3 m for three diffusers. However, both types seem to have the same effect on the change of the acoustical parameters (i.e., a reduction of EDT and T20, and an increase of C50 and C80).
Introducing even a single diffuser to any walls of such a non-diffuse room is enough to significantly change the reverberation time in the room as seen in the measurement results and confirmed by the statistical analysis. This is because when such a room is empty, the sound keeps bouncing between the walls for a considerable amount of time while the sound field is mainly in the lateral plane. However, when a diffuser is introduced on a wall, the sound energy is directed down to the floor and up to the ceiling which are highly absorptive surfaces. The role of diffusers in this particular room is therefore much greater than in a room in which all boundaries have the same material. Consistently, as the number of added diffuser increases, the faster the sound energy is directed towards absorptive boundaries (floor/ceiling), which is in fact observed in the measurement results.
The changes in the acoustical parameters observed in the measurement results are in line with the trends observed in previous studies investigating scale models when switching from a reflective to a diffuse condition [6
]. However, these results also differ from other publications [9
]. Finally, it could be generally concluded that the effects produced by scattering surfaces on the acoustic parameters depend on several factors such as the amount of diffusion already present in the space, the position of the scattering surfaces, the position and amount of the absorptive surfaces, as well as the presence of mirrored reflective surfaces. Furthermore, the size and shape of the space are important parameters influencing the sound field diffusivity [14