# Acoustic Characterization of Some Steel Industry Waste Materials
## 4 Results and Discussion  
In Figure 8, the measured sound absorption coefficient and transmission loss of the white dress wool are presented. This material features an \"S-shaped\" absorption curve with the characteristic behavior typical of porous-fibrous materials, that is low values at low frequencies and values approaching a unit value at high frequencies: in particular, \(\alpha\) starts with a value of 0.13 at 200 Hz, it linearly increases and around 1700 Hz, it reaches the unit value. The _TL_ curve is also typical for fibrous materials, it does not reach high values but at about 1250 Hz, it shows a change in slope with an increasing trend. In Figure 9, the acoustic performances of all the samples made of slag spheres of the three diameter ranges are shown in the same graph. The absorption coefficient curves of BIG and MEDIUM samples can be referred to the typical quarter wavelength resonance behavior of granular materials: the oscillations of the sound absorption for granular materials are caused by the air gap around the granules. If the gap between granules is too small or too large, not enough friction and subsequent heat transfer can develop between the air and the solid skeleton of the pore wall during the propagation of sound waves [20]. The first peaks are, respectively, at about 580 Hz for sample BIG of 100 mm length, 1330 Hz for sample BIG with 50 mm of thickness and about 1190 Hz for sample MEDIUM, which is 50 mm long. As the dimension of the sample increases, a more complex gap distribution occurs together with longer channels. While the acoustic wave propagates, the air particle collisions and the flow volume raise within the pores, resulting in a higher dissipation of energy. When the natural frequency of the spheres mix decreases, the sound absorption peak shifts to a lower frequency. Figure 7: Examples of protective layers: (**a**) top surface of the sample closed by the protective layer sealed by glue; and (**b**) protective layer. It can be observed that for the SMALL sample, a smooth absorptive behavior is present where the resonance peaks and throughs are suppressed. As stated in [31], for large grain mixes, the absorption coefficient spectrum shows an oscillating trend, corresponding to resonance maxima and minima. On the contrary, small grain mixes lose the resonant behavior, featuring a less pronounced trend. For this reason, the transmission loss of SMALL sample is higher than the one measured for the BIG and MEDIUM samples throughout the whole frequency range of interest. This may be caused by the nature of the SMALL sample, featuring spheres with \(\varnothing\in(0;0.71)\) mm. Such structure can be considered since compact sand and its higher density results in a very high airflow resistance. This gives rise to a reflective behavior. In the frequency range between 200 and 300 Hz, a drop in both \(\alpha\) and \(TL\) values of the SMALL sample were observed, probably because of the rigid frame resonance of the system. Figure 10 shows the absorption curve of the slag spheres sample embedded inside an inert material. Additionally, in this case, the graph shows the typical quarter wavelength resonance behavior of granular materials. The first peak almost reaches a unit value around 1390 Hz. The transmission loss remains quite low throughout the whole frequency range of interest. Figure 8: Acoustic properties of white dress wool sample: (**a**) sound absorption coefficient; and (**b**) transmission loss. Figure 9: Acoustic properties of slag spheres samples BIG, MEDIUM and SMALL: (**a**) sound absorption coefficient; and (**b**) transmission loss. In order to easily compare the performances of different materials, the weighted noise reduction coefficient (\(NRC\)) and the sound absorption average (\(SAA\)) [49] are used to summarize the absorption characteristics of the tested samples by single rating numbers: they range between 0 and 1, in the case of perfectly reflective or perfectly absorptive materials, respectively.