## 3 Results and Analysis
### Just Noticeable Difference (JND)  
For the calibration of the acoustic model, the absorption coefficients indicated in Table 2 were established depending on the type of material, taking as reference the values obtained by [PERSON] through standardized tests [36]. As previously stated, a 100% absorbent material was applied to the surfaces representing free field. Regarding the dispersion coefficients, in this study, three levels were established, based on the roughness of the materials, as established in Table 3. The values of these coefficients were adjusted during the calibration process of acoustic model. In this environment, the degree of detail of the decoration of the Door of the Apostles is of special importance, which notably increases the dispersion of these surfaces. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{6}{c}{**Absorption Coefficient by Frequency in Hz**} \\ \cline{2-9}  & **125** & **250** & **500** & **1000** & **2000** & **4000** & **8000** \\ \hline Marble floor & 0.01 & 0.01 & 0.01 & 0.02 & 0.02 & 0.02 & 0.02 \\ Limestone walls & 0.02 & 0.02 & 0.03 & 0.04 & 0.05 & 0.05 & 0.05 \\ Hard surfaces average & 0.02 & 0.02 & 0.03 & 0.03 & 0.04 & 0.05 & 0.05 \\ Solid wooden door & 0.14 & 0.10 & 0.06 & 0.08 & 0.10 & 0.10 & 0.10 \\ Free field & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Absorption coefficients by frequencies of the materials used in the acoustic simulation. Figure 5: Frequency variation of T30 (**a**) and EDT (**b**) measurements. Figure 6: Frequency variation of C80 (**a**) and C50 (**b**) measurements. The validation of the acoustic model was performed using the JND of parameters C80 and C50. The ISO 3382-1 [17] standard sets the JND for parameter C80 to 1 dB. However, there are authors who have determined higher values of this threshold from experimental studies. [PERSON] et al. established a JND of \(1.6\pm 0.3\) dB for parameter C80 [37]. [PERSON] et al. placed the JND for C80 in real sound fields around 2.5 dB [38], results that were confirmed by [PERSON] by using synthetic sound fields [39]. Regarding parameter C50, the standard does not indicate a specific value of the JND differential threshold. However, there are experimental studies that have analyzed the minimum differences of this parameter in order to be perceived by the human ear. [PERSON] et al. estimated a JND of 1.1 dB, with an increase of approximately 3 dB being necessary to create an easily detectable improvement in everyday situations [40]. With all this, it is important to note that today there is no definitive consensus accepted by the entire scientific community [41]. Taking into account the investigations analyzed, in this study, the JND for the parameters C80 and C50 were established at 2.5 dB for the calibration of the acoustic model. Comparing measurement with ODEON simulation for all points, for parameter C80, we found that 87% of measuring points have a JND equal to or less than unity, the most unfavorable value being 1.38. For parameter C50, said percentage is 93%, all values being below 1.2. In average values, JND of both parameters is less than unity, taking for C80 the value of 0.59 and for C50 the value of 0.40. Figure 7 shows the dispersion of the JDN values of C80 and C50 with ODEON simulation for each of the sound sources (A-I). The locations of the different judges of the different irrigation ditches correspond to the letters B to I in Figure 1a. These locations correspond to the measurements taken in the cultural heritage environment. The location of the bailiff is next to the position of A. Comparing the measurement with the simulation in CATT-Acoustic, for parameter C80 we find that 81% of measuring points have a JND equal to or less than one, presenting the most unfavorable value at this point (1.47). For parameter C50, said percentage is 83%, the most unfavorable value being 1.35.