## 2 Materials and Methodologies  
### Generalities and Test Conditions  
The acoustic barriers herein investigated were realized in a 1:10 model [23] that was tested by considering 1/3-octave bands from 1 kHz to 15 kHz, equivalent to the range 100-1000 Hz in the case of a real scale [24; 25; 26].  
Acoustic measurements were undertaken inside a semi-anechoic chamber, to be 4.40 \(\times\) 4.40 \(\times\) 4.50 m (L \(\times\) W \(\times\) H), composed of absorbing materials on walls and MDF boards on the floor and having a cut-off frequency equal to 100 Hz, according to [PERSON]'s theory [27]. The arrangement of placing hard floor finishes with MDF boards simulates the real configuration of a road environment, having acoustic barriers on the sides. On this basis, the acoustic measurements consider both direct and reflected soundwaves.  
The results were analyzed in terms of insertion loss (_IL_), considered as the configuration difference between the sound pressure level measured without any obstacle (\(L_{FF}\)) and with the presence of a barrier (\(L_{Bar}\)) [28], as indicated in Equation (2).  
\[IL=L_{FF}-L_{Bar}\ (\text{dB}) \tag{2}\]  
In terms of notation, Equation (2) derives from the ratio of the incident wave \(p_{inc}\), which can be either plane or cylindrical, and the total field \(p(r)\), as indicated in Equation (3).  
\[IL=20 log_{10}\left|\frac{p_{inc}}{p(r)}\right|\ (\text{dB}) \tag{3}\]  
In a controlled environment like an anechoic chamber, the diffraction of the lateral edge of the barriers can be considered negligible, as well as all the other factors (e.g., air absorption, wind speed, temperature variance, etc.) that contribute to modifying the spreading of the sound waves. On this basis, the results should be considered as more optimistic than the true effects of a real environment.  
By considering _Xs_ and _Xr_ as the distance occurring between the source or the receiver and the edge of the barrier, as shown in Figure 3, the dimensions used for the first set of measurements are the following:  
- \(X\)s = 800 mm;  
- \(Xr\) = 800 mm.  
For the second set of measurements, the following dimensions of \(X\)s and \(Xr\) were used:  
- \(Xs\) = 400 mm;  
- \(Xr\) = 800 mm.  
The third set of measurements was carried out in order to visualize the spatial distribution of the IL modeled on the receiving side.  
Given the employment of an omnidirectional sound source, instead of a linear array loudspeaker, the limits of these tests were optimized by moving the receiver across an x-y plan (without any height alteration) in order to create different directivity angles. For this scope, Figure 4 indicates in plan the disposition of the equipment during the assessment. The position of the receiver follows a regular grid having a distance between nodes equal to 200 \(\times\) 200 mm. On this basis, the microphone was moved to 25 positions, while the sound source was fixed on the central axis of the barrier at an 800 mm distance. This methodology was adopted to simulate the movement of a linear source, as the road traffic would be.  
Where the scatterers have a diameter of 15 mm (A), the centered distance between wooden sticks is 30 mm (2A). Where the cylindrical elements have a diameter of 9 mm (B), the centered distance between wooden sticks is 18 mm (2B).