## 3 Auditory Perception Study of Sound Field in Closed Spaces with Different Structural Parameters
### Experimental Results  
#### 3.3.1 Summary of Results  
First of all, analysis of variance (at significant level of \(\alpha\) = 0.05) for the evaluation data given by all the participants proves that the effect (difference among the testing stimuli) is statistically significant (\(p\) = 0.0095 < 0.05). The testing stimuli have significant effect on the participants. The listening test is valid. All the evaluation data given by the subjects are collected to perform cluster analysis to judge the validity of the evaluation results (as seen in Figure 5). For this tree diagram, the y-axis denotes the distance of among each class in the cluster analysis. It refers to the difference among each class; the greater the distance, the greater the difference between the subject's evaluation result and other subjects'. According to the results of the cluster analysis, the evaluation data of No. 13 and No. 9 are significantly different from the evaluation results of other subjects, and should be eliminated. The rest of the data is valid in the subjective evaluation experiment. For the three cuboid closed spaces, with volumes of 24 m\({}^{3}\), 96 m\({}^{3}\), and 192 m\({}^{3}\) (each with a thick pit sand mortar polished brick wall), the absolute variations of the corresponding space volume are \(|\mathrm{V_{a}-V_{b}}|\) = 72 m\({}^{3}\), \(|\mathrm{V_{b}-V_{c}}|\) = 96 m\({}^{3}\), and \(|\mathrm{V_{c}-V_{a}}|\) = 168 m\({}^{3}\), respectively. The subjective test results of spatial auditory perception changes caused by volume are shown in Figure 6.  
Figure 5: Cluster analysis of subjective experimental results. In the figure, the x-coordinate and the y-coordinate denote the subject number and the calculated distance, respectively. The larger the distance, the greater the difference between the participant’s evaluation result and other participants’. It can be seen from Figure 6 that, for the three different musical sounds, when the spatial volume changes, the influence in different receiving points on hearing is not obvious. When the volume is changing, the auditory perception of the flute music and the violin music change. Generally, the smaller the volume, the better the auditory perception of flute music and violin music will be. As for the symphony sound, its auditory perception does not change obviously in different spatial volumes. For the four closed spaces, with absorption coefficients of 0, 0.5, and 1 (cases d, e, and f, respectively), and the inner surface of thick pit sand mortar polished brick (the absorption coefficient of the wall is a function of frequency, case c) in the same volume and shape, their sound absorptions are 0 m\({}^{2}\), 104 m\({}^{2}\), 208 m\({}^{2}\), and 31.98 m\({}^{2}\), respectively (where \(\alpha\) of space c is calculated according to GB_T 3947-1996). The absolute variations of the corresponding spatial sound absorption are \(\left|\mathrm{E_{d}-E_{c}}\right|\) = 31.98 m\({}^{2}\), \(\left|\mathrm{E_{e}-E_{c}}\right|\) = 72.02 m\({}^{2}\), and \(\left|\mathrm{E_{f}-E_{c}}\right|\) = 176.02 m\({}^{2}\). The subjective test results of the changing of the spatial auditory perception caused by the inner surface absorption coefficient are shown in Figure 7.  
It can be seen from Figure 7 that when the inner surface absorption coefficient is changed, the spatial hearing changes caused by different receiving points of the three musical sounds are not obvious. In the extreme case of \(\alpha\) = 0, the hearing effects of the three musical sounds are the worst. For flute music, when \(\alpha\) = 1 the hearing effect is the best. For violin music, in the cases of \(\alpha\) = 0.5 and \(\alpha\) = 1, the hearing effect is relatively good with no obvious difference. For symphony music, in the three cases of \(\alpha\) = 0.5, \(\alpha\) = 1, and thick pit sand mortar polished brick wall surface, there is no obvious difference in hearing effect.