# A Novel Acoustic Ventilation Barrier Based on the Block-Shaped Space-Coiling Metamaterial
## 4 Experimental Validation of the Numerical Simulation  
In order to validate the numerical simulation method adopted in this research, an experimental test on the TL of a full-scale meta-unit sample was performed. The transfer matrix method was adopted to measure the transmission loss of the meta-unit by using an impedance tube (shown in Figure 7). The sample used in the experiment was manufactured through 3D printing using photosensitive resin material (shown in Figure 7b), whose design parameters are listed in Table 3. Figure 7c shows the real set-up of the experimental test in which Beijing Shengsheng Acoustic and Electrical Technology Co., Ltd.'s BSWA F100 impedance tube (Beijing, China) was used. Since the inner size of the test tube is fixed at 100 mm, the outer side length of the printed meta-unit sample was also set to 100 mm. In the test, the sample was fixed on the sample holder in the middle of the impedance tube. The speaker at the initial end of the impedance tube generated a wide band of sound waves, which propagated toward the anechoic termination. Due to the small diameter of the tube, the sound waves can be approximately regarded as planar waves. The input and output acoustic pressures are measured by four microphones in which the input acoustic pressures were obtained from the mean acoustic pressures measured using Mic 1 and 2, and the output acoustic pressures were the mean acoustic pressures measured using Mic 3 and 4 (shown in Figure 7a). And the values of the TL were computed as follows:  
\[\text{TL}=-20\log_{10}\lvert\tau_{P}\rvert \tag{2}\]  
where the acoustic pressure parameter is computed by  
\[\tau_{p}=\frac{\sin(kS_{1})}{\sin(kS_{2})}\cdot\frac{p_{3}e^{jkS_{2}}-p_{4}}{ p_{1}-p_{2}e^{-jkS_{2}}}e^{jk(L_{1}+L_{2})} \tag{3}\]  
where \(p_{1}\), \(p_{2}\), \(p_{3}\), and \(p_{4}\) are the acoustic pressures measured from Mic 1, Mic 2, Mic 3, and Mic 4, respectively; \(S_{1}\) and \(S_{2}\) are the spacings between the microphones, which were both set to 100 mm; and \(L_{1}\) and \(L_{2}\) are the distances between the corresponding microphones to the sample, which were set to 100 mm identically.  
The experimentally measured TL is shown in Figure 7, and it is further compared to the corresponding numerical simulation result obtained from COMSOL Multiphysics. It is seen from Figure 8 that the TLs obtained from the numerical simulation are close to the corresponding experimental results, validating the numerical simulation method adopted in this research. It is noted that there exist discrepancies between the TL peaks obtained from numerical simulations and those from experimental tests, and a similar phenomenon is also found in [21]. Such a discrepancy was mainly triggered by the increased viscosity and heat losses in the practical measurements. In addition, both the test sample and the impedance tube are not perfectly acoustically rigid, while the corresponding model in the numerical simulation is regarded as acoustically rigid, contributing to the discrepancies between experimental results and the corresponding numerical simulation ones. However, in a general sense, the numerical simulation results are almost in agreement with the corresponding experimental ones.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{L}\) & \(\mathbf{l}\) & \(\mathbf{w}\) & \(\mathbf{d_{1}}\) & \(\mathbf{d_{2}}\) & \(\mathbf{d_{3}}\) \\ \hline
100 mm & 50 mm & 1 mm & 8 mm & 8 mm & 8 mm \\ \hline \end{tabular}
\end{table}
Table 3: The design parameters of the 3D-printed full-scale meta-unit sample.