## 2 Materials and Methods  
### Reverberation Time  
Reverberation time is a key parameter when it comes to acoustics in confined spaces. This is the decay of the sound following the switching off of a source and due to the sound reflections, that continue to travel in the space. The sound energy that affects a surface S is divided into three components: a part is reflected by the surface, a part is absorbed, and a part transmitted beyond the material [15; 16; 17]. Before the sound emitted from a generic source reaches the receiver, a time, called the sound wave propagation time, passes, equal to the ratio between the distance of the source from the receiver and the speed of sound. The receiver will receive various contributions deriving from the source, those related to direct sound and those due to reflections. [PERSON] defined this parameter at the end of the 1800s as: given an interrupted stationary source, the reverberation time is the time between the instant in which the direct sound ends and the instant in which the sound level has dropped by 60 dB [18], as shown in Figure 1. In a room, the longer the reverberation time, the greater the contribution of the components of the reflected sound compared to the direct one. The absorption of the materials changes with the frequency, so the reverberation time also varies at the different frequencies considered. In architectural acoustics the frequencies in the octave bands from 125 to 4000 Hz are considered. Frequencies above 4000 Hz are not considered because sound absorption by air prevails. Frequencies below 125 Hz are not considered because the human ear has a reduced sensitivity at low frequencies. [PERSON], through a series of experiments, found that the value of this parameter (RT\({}_{60}\)) depended on the volume of the space and the total absorption of its internal surfaces. With the same shape of the confined space, the reverberation time increases linearly as the size increases. According to [PERSON], the reverberation time value is a function of the room volume and the total sound absorption of its internal surfaces [18] as descripted in the following equation:  
\[T_{60}=0.161\times\ \frac{V}{\sum_{i=1}^{N}\alpha_{i}\times S_{i}} \tag{1}\]  
Here:  
* T\({}_{60}\) is the time in seconds required for a sound to decay 60 dB
* 0.161 is a dimensioned factor (s/m)
* V is the volume of the room in m\({}^{3}\)
* \(\alpha_{i}\) is the i-th sound absorption coefficient
* S\({}_{i}\) is the i-th surface in m\({}^{2}\) with a \(\alpha_{i}\)  
The sound absorption coefficient is a number that varies between 0 and 1:0 indicates absence of absorption, that is the surface is totally reflective, while 1 indicates total absorption without reflection. The sound absorption coefficient is used to evaluate the sound absorption efficiency of the materials. It is defined as the ratio of absorbed energy to incident energy. The measurement techniques of this parameter are essentially two for normal and random incidence. The measurement of the sound absorption coefficient for normal incidence is performed in a Kundt tube in accordance with ISO 10534 [19] to know the percentage of sound absorbed by a material. It is the only test in which there is no margin of discretion in the setup phase, since it is a sample of material inserted into a tube and hit by a direct wave. The measurement of the sound absorption coefficient for random incidence is performed in a reverberation room in accordance with ISO 354 [20] to calculate the percentage of sound absorbed by a product hit by waves from various directions, simulating a situation of real use. The test setup can affect the result since the absorption of a panel also depends on its position within a room such as the distance from rigid surfaces and the distance between panels. Figure 1: Diagram for the evaluation of the reverberation time (RT\({}_{60}\)) using the natural decay curve of a sound signal.