## 2 Study Methodology  
### General Settings  
[PERSON]'s [18] study found that in the frequency bands higher than the Schroeder frequency, geometric acoustics can be used to calculate the indoor sound field. In geometric acoustics, the reflection and scattering of sound rays are used to simulate the sound propagation process. This method has a high accuracy at high frequencies where the surface size is much larger than the wavelength. [PERSON] et al. [19] reported the calculation results of the Eyring formula after adding scattering in different space shapes. The CATT calculation results when the scattering coefficient was set to 0.4 were compared with the measured results. The \(RT\) results using the three methods were in good agreement. Both the \(RT\) and Sound Pressure Level (SPL) were investigated in cubic rooms by [PERSON] and [PERSON] [20]. For uniformly distributed absorption coefficients, both the Eyring diffusion and modified diffusion models demonstrated good agreement with the CATT model. These research results indicated that the computer simulation can to a certain extent reflect the influence of surface scattering on the \(RT\) in real space. It has a good reliability to explore the influence of surface scattering on the \(RT\) in ordinary spaces using the sound ray method. Using Odeon, CATT, and Raven software, [PERSON] and [PERSON] [21] performed computer simulations of 480 rectangular concert halls and analyzed the relationship between \(T_{30}\) and scattering. They found that \(T_{30}\) tended to decrease after diffusers were added to the walls and ceilings. [PERSON] et al. [22] indicated that the input modes of scattering parameters are different in CATT and Odeon. If the same frequency dependent scattering value assumed automatically in Odeon is applied to CATT for simulation with the same surface absorption coefficients, the \(T_{30}\) value obtained is consistent with Odeon's calculation result. In this study, we used this method to compare the CATT and Odeon in a rectangular space and a specially shaped space (through the inclined surface to eliminate the parallel planes). It is found that with the same absorption coefficient and scattering coefficient, the difference in \(T_{30}\) calculated by the two software packages is less than 5%. Referring to the international itinerant comparison of computer simulations, [PERSON] [23] and [PERSON] [24; 25] used 5% as the subjective threshold of relative difference in \(T_{30}\). Therefore, the calculation results of the two software packages are consistent. CATT Acoustic v9 is a room acoustic simulation software package that offers three different cone-tracing algorithms for source-receiver echograms and impulse responses and one audience area mapping algorithm. When the order \(\leq\) n, diffuse and specular reflections are deterministic (n = max split order) and the diffuse reflections are created by actual diffuse ray separation. The n + 1 order reflections are randomly determined by the scattering coefficient. Diffuse reflection is frequency dependent, individually tracing for each 1/1-octave 125-16 kHz [26; 27]. In CATT, the sound absorption and scattering coefficients are set for the six octave bands from 125 Hz to 4 kHz. For example, \"ABS ceiling = \(<\)\(\alpha\)125 \(\alpha\)250 \(\alpha\)500 \(\alpha\)1k \(\alpha\)2k \(\alpha\)4k \(>\) L \(<\) s125 \(\alpha\)500 s1k s2k s4k \(>\)\". The sound absorption and scattering coefficients are expressed by 1%-99%. The scattering coefficients of different surfaces can be set directly according to the test data or as suggested by the CATT user manual [26; 27]. Since the scattering coefficient in the CATT can be set separately for each frequency band, the CATT was used as the calculation tool in this study. In the simulated calculation, a shoebox-shaped small theater was used as the basic model for calculation and analysis. Its three-dimensional size was 25 \(\times\) 16 \(\times\) 7.5 m (L \(\times\) W \(\times\) H), and its indoor volume was 3000 m\({}^{3}\).