## 3 Experimental Verification  
Two verifying experiments were conducted: an insertion loss experiment and a distance attenuation experiment. In the experiments, vehicle noise was recorded next to the roads and subsequently played in the audio amplifier to emulate a point sound source that was used to measure actual insertion loss of noise barrier. For every type of car at different speed range, the synthesized point source consisted of five recorded audio samples. The length of each audio sample is 8 s.  
The insertion loss experiment was conducted to collect sound level pressure data in front of and behind the noise barrier. A schematic of the experiment is shown in Figure 3.  
Two noise recorders were installed, one at measurement site 1 and the other at measurement site 2, to collect noise data and compute the noise levels \(L_{1}\) and \(L_{2}\), respectively. The insertion loss of barrier is the difference between \(L_{1}\) and \(L_{2}\). The computed equivalent noise levels are shown in Table 2.  
To obtain the actual value of diffraction, noise attenuation as a function of distance between the two measurement sites should be considered. The noise data were measured in an open space near the sound barrier to avoid possible errors introduced by the change of the experimental locations. Because noise attenuation with distance is independent of the frequency of the sound source [20], the sound source audios were merged into three categories in the experiment: heavy car, middle car, and light car. The geometric configuration of measurement is shown in Figure 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Speed (km/h)**} & \multicolumn{2}{c}{**Light Car**} & \multicolumn{2}{c}{**Middle Car**} & \multicolumn{2}{c}{**Heavy Car**} \\ \cline{2-7}  & \(\mathbf{L_{1}}\) & \(\mathbf{L_{2}}\) & \(\mathbf{L_{1}}\) & \(\mathbf{L_{2}}\) & \(\mathbf{L_{1}}\) & \(\mathbf{L_{2}}\) \\ \hline \([0,40)\) & 75.21 & 46.31 & 84.26 & 52.11 & 83.91 & 54.38 \\ \([40,50)\) & 80.69 & 48.98 & 83.85 & 52.42 & 80.12 & 48.84 \\ \([50,60)\) & 80.09 & 49.03 & 86.59 & 53.76 & 85.95 & 53.39 \\ \([60,70)\) & 82.17 & 50.14 & 85.53 & 53.99 & 86.68 & 54.17 \\ \([70,80)\) & 82.74 & 50.65 & & & & \\ \(\geq\)80 & 85.30 & 52.48 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Noise levels computed in the insertion loss experiment (dB). Figure 3: Insertion loss experiment. Noise recorders were installed in measurement site 1 and measurement site 2. The data are summarized in Table 3. Noise attenuation with distance for heavy, middle, and light vehicles are 11.16 dB, 11.03 dB, and 11.13 dB, respectively. The average of the three is defined as \(\Delta L\). In this instance, \(\Delta L=11.11\) dB. From the experimental verification, the actual value of diffraction by barrier was determined as follows (Equation (9)):  
\[\Delta L_{d}=(L_{1}-L_{2})-\Delta L \tag{9}\]  
The theoretical value of diffraction is defined as (Equation (10))  
\[\Delta L^{\prime}_{d}=\left\{ \begin{matrix}20\text{lg}\frac{\sqrt{2\pi N}}{ \tanh\sqrt{2\pi N}}+5 dB&,N>0\\ 5 dB&,N=0\end{matrix} \right. \tag{10}\]  
where \(N\) is the Fresnel number, \(N=\frac{\delta\cdot f}{\Gamma 0}\). Equations (9) and (10) are mainly applied to near-field conditions. According to reference [20], Equation (11) should be satisfied (Equation (11)). \[D<2d^{2}/\lambda \tag{11}\]  
where \(D\) is the distance from the sound source to the receivers' center, \(d\) is the step of the receivers, and \(\lambda\) is the wave length. The speed of sound is 340 m/s. In the experiment, \(D\) is calculated as approximately 5.26 m, \(d\) is set as 0.5 m in environmental acoustics calculation, and the wave length \(\lambda\) is in a range of [2.125, 0.054] with a primary frequency range of 160 Hz to 6300 Hz. Thus, Equation (11) is satisfied. The experimental setup can be considered with the theoretical formulation of the Fresnel number \(N\).