## 4 Results and Discussion
### Phenomenological Model Simulation  
After analyzing the measurement results, we proceeded to numerical simulation using the models described in detail above. As a first model, we adopted the model based on [PERSON]'s [10] studies. As already anticipated, this model requires knowledge of three parameters: resistivity, porosity, and structure factor. The sound absorption coefficients were calculated for each of the available frequencies in the measured values. Figure 7 shows the measured sound absorption coefficient values and those simulated with the Hamet model.  
Analyzing Figure 7, it is possible to notice that the Hamet model can simulate the acoustic behavior of the material with different performances. The structure factor containing the information on the first maximum of the trend obtained from the measured data makes the Hamet curve consistent with the measured data. The greatest analogy between measured and simulated data occurs for the type of fragments containing only the wooden part. The 4 cm thick sample has a bell-shaped pattern, with the simulated data approaching those measured at low frequencies. The 8 cm thick sample shows a trend with a double maximum as reported by the measured data. The first maximum of the Hamet curve is positioned at the same frequency as the measured data as specified in the structure factor, but the values of the acoustic coefficient are greater. In this case, the simulated data are closer to those measured at low frequencies.  
Let us now analyze the data obtained with the mixed fragments; also, in this case, the Hamet curve has a shape like that assumed by the measured data. The structure factor once again allows us to adequately position the maximum of the Hamet curve. The 4 cm thick sample has a bell shape with the simulated data which are maintained at approximately the same distance from those measured throughout the frequency interval. This behavior can be justified by a difference in the resistivity value; in fact, the Hamet model seems to refer to a lower resistivity value. The 8 cm thick sample has a bell-shaped pattern with a tail with an increasing pattern at high frequencies. Again, the simulated data is maintained at approximately the same distance from the measured data throughout the frequency range. An approach is noticeable only near the maximum.  
Figure 7: Sound absorption coefficient values comparison between measured and simulated. The figure shows a 4 cm thick sample (**a**,**c**,**e**) and 8 cm thick sample (**b**,**d**,**f**) for only the wooden part (**a**,**b**), mixed (**c**,**d**), and only bark (**e**,**f**).  
Finally, we analyzed the data obtained with the fragments containing only bark; in this case, the Hamet curve has a shape like that assumed by the measured data. The 4 cm thick sample has a bell shape with the simulated data approaching those measured only at low frequencies. The 8 cm thick sample has a bell-shaped pattern with a tail with an increasing pattern at high frequencies. In this case, the simulated data is maintained at approximately the same distance from the measured data throughout the frequency range. An approach is noticeable only immediately after the peak of the Hamet curve.  
To compare the results of the numerical modeling, we calculate the performance metrics of the model. Table 2 shows the Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and the Person's correlation coefficient for the Hamet model.