# Acoustic Characterization of Some Steel Industry Waste Materials
## 5 Conclusions  
In this paper, the acoustic characterization of some steel industry waste materials derived from black and white slags is provided. The measurements performed by using a four-microphone impedance tube allowed us to obtain the acoustic properties of the tested samples. As a result, the analyzed materials can be mainly considered as porous media featuring interesting sound absorption and insulation characteristics. The wool derived from white dress exhibits a trend of the sound absorption which is typical of fibrous material, while slag spheres and encapsulated spheres behave as granular materials, with an oscillating tendency whose peaks are due to the resonance of the particle frame at a frequency corresponding to the one of a quarter wavelength resonator having the same thickness. Only the SMALL sample showed a more insulating than absorptive behavior, due to its higher density and airflow resistance values. It can be said that the SMALL sample acoustically behaves like compact sand. In order to determine the non-acoustic parameters of the samples, without the possibility of performing direct measurements, an inverse characterization technique was applied. Based on the JCA model, the inverse technique used relies on a standard iterative optimization procedure: the minimization is performed between the sound absorption coefficient measured in a four-microphone impedance tube and the one estimated by optimizing the inversion values into the JCA model. The optimization intervals were set according to the literature data. The five resulting non-acoustic parameters are compatible and comparable with the ones which can be found in other studies dealing with porous and granular media. The fact that some samples are made by spheres assembled by ranges of diameters and not by single diameter values explains possible discrepancies with literature data. The next step of the research will be focused on the validation of the inversion procedure and of the optimized non-acoustic parameters, by means of specific experimental measurements. Further investigations on the microstructure and the particle arrangements will allow the optimization and customization of the material for specific noise control applications.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \(d\) & \(\Phi\) & \(\sigma\) & \(\kappa_{\infty}\) & \(\Lambda\) & \(\Lambda^{\prime}\) \\  & **(mm)** & **(-)** & **(Pa \(*\)s/m\({}^{2}\))** & **(-)** & **(\(\mu\)m)** & **(\(\mu\)m)** \\ \hline White dress wool & 50 & 0.87 & 10550 & 1 & 114 & 209 \\ Slag spheres “BIG” & 100 & 0.50 & 10600 & 1.46 & 182 & 333 \\ \(\varnothing\in[1.4;2.0)\) mm & 50 & 0.52 & 11350 & 1.33 & 164 & 301 \\ Slag spheres “MEDIUM” & 50 & 0.44 & 30250 & 1.47 & 115 & 211 \\ \(\varnothing\in(0.71;1.4)\) mm & & & & & & \\ Slag spheres “SMALL” & 50 & 0.39 & 144550 & 4 & 92 & 169 \\ \(\varnothing\in(0;0.71)\) mm & & & & & & \\ Encapsulated spheres & 50 & 0.52 & 9100 & 1.37 & 186 & 512 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Inversely determined non-acoustic parameters.  
**Author Contributions:** Investigation, data curation, writing--original draft preparation, visualization, E.L. Methodology, resources, supervision, E.A.P. Software, S.S. Conceptualization, writing--review and editing, E.A.P. and E.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The authors would like to thank [PERSON] (Brescia), particularly [PERSON], for providing the material and technical insight on the manufacturing and inertiaation processes.  
**Conflicts of Interest:** The authors declare no conflict of interest.