# Acoustic Characterization of Some Steel Industry Waste Materials
## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & & & & \\ \cline{2-13} \multirow{2}{*}{**Material**} & **200** & **250** & **315** & **400** & **500** & **630** & **800** & **1000** & **1250** & **1600** & **2000** & **2500** & **3150** & **Average** \\  & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** & **Hz** \\ \hline Wool-50 & 5.55 & 12.95 & 14.98 & 13.30 & 7.33 & 2.13 & 0.01 & 1.03 & 0.63 & 0.35 & 1.79 & 4.48 & 4.85 & 5.34 \\ BIG-100 & 13.26 & 6.33 & 0.24 & 4.53 & 4.98 & 0.90 & 2.53 & 0.75 & 1.77 & 1.03 & 0.12 & 1.93 & 7.59 & 3.54 \\ BIG 50 & 14.22 & 16.27 & 16.13 & 5.75 & 0.26 & 1.59 & 1.19 & 1.40 & 0.83 & 1.05 & 0.14 & 2.49 & 4.86 & 5.09 \\ MEDIUM-50 & 17.09 & 14.75 & 10.97 & 5.82 & 8.18 & 7.30 & 6.13 & 2.93 & 0.36 & 1.33 & 1.34 & 3.61 & 3.03 & 6.37 \\ SMALL-50 & 13.91 & 18.75 & 17.70 & 15.65 & 8.41 & 2.27 & 0.94 & 2.07 & 5.19 & 4.96 & 0.42 & 6.47 & 10.48 & 8.25 \\ Encapsulated-50 & 10.8 & 7.93 & 13.04 & 18.00 & 18.78 & 12.01 & 3.91 & 3.06 & 2.81 & 1.34 & 1.26 & 6.30 & 9.73 & 7.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative errors for third octave bands and average values of the relative errors. In Figure 12, the experimental and predicted curves are depicted for the three slag spheres samples: BIG, MEDIUM and SMALL. The predictions referring to BIG and MEDIUM samples are in good agreement with the experimental curves, showing the classic resonant behavior. In particular, sample BIG--50 features a high degree of agreement between the two curves above 500 Hz. In the high frequency range, a slight discrepancy can be observed for sample BIG--100. For the sample SMALL, the estimated curve fairly approximates the measured curve, but it does not follow the trend in an optimal way along the entire frequency range. This is probably caused by the nature of the SMALL sample, which is neither an absorbing nor an insulating material. Figure 13 shows, overall, a good correspondence between the estimated and the measured absorption curves relative to the sample made of encapsulated slag spheres. Figure 12: Comparison between experimental and predicted sound absorption coefficients for slag spheres samples BIG, MEDIUM and SMALL. Blue lines are referred to the respective JCA fittings. Figure 13: Comparison between experimental and predicted sound absorption coefficient for the sample made of encapsulated spheres. Table 4 summarizes the values of the five non-acoustic parameters obtained by applying the optimization procedure. The achieved parameters seem to be consistent with what can be found in the literature for similar materials. Nevertheless, in [21], the authors stated that the porosity of the random close packing of spherical beads should remain constant to a value of approximately 0.36, when the ratio between the sample holder diameter and the tested spheres diameter exceeds the value of 10. This corresponds to the characteristics of the case at hand, since the internal diameter of the sample holder is 46 mm and the diameter of the largest spheres is 2 mm. However, the discrepancies may be due to the fact that, in this study, the spherical particles have not a single diameter value, but they are indeed assembled in diameter ranges, thus, the internal arrangement may be different from the one described in [21]. In order to completely validate the optimal parameters identified by the inverse technique, the next step of the research will be the direct experimental measurement of the five non-acoustic parameters.