# Characterization of Natural Gypsum Materials and Their Composites for Building Applications
## 2 Materials and Methods
### Acoustic Performance  
The acoustic properties of samples manufactured by mixing each gypsum (Agadir and Safi) powders and water were measured by means of an impedance tube ([PERSON]'s tube, Bruel & Kjaer, model 4206; 1/4 inch microphones Bruel & Kjaer, model 4187) available at the University of Perugia, according to ISO 10534-2 standard [24]. Cylindrical samples of AG and SG gypsums with diameters of 29 mm and 100 mm (Figure 3) were characterized in terms of sound absorption and sound insulation properties. For each kind of gypsum, two samples of the smaller-diameter were available for testing, while only one 100-mm-diameter sample was available, due to the difficulty in fabrication and transportation of the material without cracks and inhomogeneity.  
The main features of the considered samples are reported in Table 2. The density of the samples was calculated weighing them with an electronic precision balance and assuming perfect cylinders of the specified diameter. The thicknesses of the 100 mm samples was higher than the ones of the 29 mm samples (about 25 mm compared to 21 mm); the larger samples were characterized by a lower density (1630 and 1520 kg/m\({}^{3}\) for Agadir and Safi gypsum, respectively) with respect to the smaller  
Figure 3: The investigated gypsum of Agadir and Safi cylindrical samples for the large and small tube.  
ones, which have a density in the 1830-1870 kg/m\({}^{3}\) range. No significant difference was found between densities of the Agadir and Safi gypsums.  
The normal incidence absorption coefficient was measured in the 100-1600 Hz (large tube) and 400-5000 Hz (small tube) frequency range, using the transfer function method with a two microphone configuration, according to [24].  
The sound pressure was measured at the same time in the two fixed microphone positions and the calculation of the transfer function between them (H\({}_{12}\)) was carried out. The normal incidence absorption coefficient is given by Equation (8):  
\[\alpha=1-|r|^{2} \tag{8}\]  
where \(r\) is the reflection factor depending on the transfer function for the incidence (\(H_{I}\)) and the reflected \(H_{R}\) wave, the wavenumbers (\(K_{0}\)), and the distance between the top of the sample surface and the microphone position \(x_{1}\), as shown in (9):  
\[\mathbf{r}=\left[\frac{H_{12}-H_{I}}{H_{R}-H_{12}}\right]\exp(2 iK_{0}x_{1}) \tag{9}\]  
A four microphone transfer function method is used in order to evaluate the acoustic insulation properties of the material (TL, transmission loss); TL is measured in the 400-5000 Hz frequency range by the two-load method, with two consecutive acquisitions for each sample at different conditions of the tube extremity (a reflective and an absorbing material are installed on the terminal part of the tube in each acquisition) [25; 26]. TL is related to the sound transmission coefficient \(\tau\) as:  
\[TL=10\cdot\log(^{1/\tau}) \tag{10}\]  
The experimental apparatus in the large and small tube configurations during the acoustic absorption and transmission loss measurements is shown in Figure 4; several measurements for each sample were carried out for the same disk, by modifying their position inside the tube, and a mean value of \(\alpha\) and TL were considered.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Thickness [mm]** & **Diameter [mm]** & **Density [kg/m\({}^{3}\)]** \\ \hline AG-1\_1 & 25.1 & 100 & 1630 \\ SG-1\_1 & 25.6 & 100 & 1520 \\ AG-s\_1 & 21.3 & 29 & 1860 \\ AG-s\_2 & 21.6 & 29 & 1860 \\ SG-s\_1 & 20.4 & 29 & 1830 \\ SG-s\_2 & 20.9 & 29 & 1870 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of the examined samples for acoustic measurements.  
Figure 4: Normal incidence absorption coefficient (**a**) and transmission loss (**b**) measurements: large (left) and small (right) tube configurations.