## 4 Simulation Results and Discussion
### HR for the Resonance Frequency of 500 Hz  
Figure 4a shows the HR in a channel based on the dimensions in Table 2, and it has a relatively large cavity compared to other elements. The predicted value, 17.3 dB, of the transmission loss in Figure 4b revealed the peak at the targeted frequency of 500 Hz. Figure 3: Prototype of the slit-type soundproof panel and schematic diagram of the HR: (**a**) Prototype module of the slit-type soundproof panel; (**b**) Schematic of the slit-type soundproof panel; (**c**) HR for the panel design. The effects of cavity, neck, and duct shape changes while maintaining the same cross-sectional area using a scale factor ranging from 0.4 to 1.6 for the transverse length are investigated. Figure 5 shows the simulation result. Note that details of the numerical study cases are summarized in Table 3.  
Figure 4: The HR of 500 Hz resonance frequency: (**a**) A three-dimensional model of HR; (**b**) Predicted transmission loss. Figure 5: The shape variation effects on the transmission loss of the HR with the resonance frequency of 500 Hz: (**a**) variation in cavity shape; (**b**) variation in neck shape; (**c**) variation in duct shape; (**d**) comparison with the optimized and the baseline models. In Figure 5, it is observed that, even with the identical cavity, neck, and duct area, the shape variation can cause the change in transmission loss. In Figure 5a, it is observed that, as the cavity ratio is reduced, the peak frequency and magnitude of the transmission loss decrease. When the cavity ratio grows, the magnitude of the transmission loss increases without frequency shift. This means the cavity ratio should be close to or greater than 1.0 to avoid frequency shift and achieve better noise reduction. When the neck ratio changes, the frequency shifting phenomenon can be observed at the lower as well as the higher neck ratio, and no notable trend can be found in the magnitude of the transmission loss, as shown in Figure 5b. In Figure 5c, it can be seen that, as the duct ratio is reduced, the peak frequency and magnitude of the transmission loss decrease--the same trend as the cavity ratio. Additionally, as the duct ratio increases, the magnitude of the transmission loss increases without frequency shift. Note that the peaks of transmission loss curves are increased up to 25.6 dB, 32.9 dB, and 57.5 dB for the shape variation of the cavity, neck, and duct, respectively. From the results, the most dominant factor influencing the peak value of transmission loss is the shape of the duct, but in the panel design, we decided to keep it unchanged for preserving air-transpassing capability. Thus, in designing the optimal model for the maximum transmission loss, two parameters, cavity and neck shapes, are considered using  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**(a) Cavity—Figure 5a**} \\ \hline
**Designation** & **Scale Factor** & **L\({}_{\text{c}}\) (mm)** & **H\({}_{\text{c}}\) (mm)** & **Cavity Ratio (L\({}_{\text{c}}\)/H\({}_{\text{c}}\))** & **A (mm\({}^{\text{2}}\))** \\ \hline Cavity 1 & 0.4 & 40 & 275 & 0.145 & 11,000 \\ \hline Cavity 2 & 0.6 & 60 & 183.33 & 0.327 & 11,000 \\ \hline Cavity 3 & 0.8 & 80 & 137.50 & 0.582 & 11,000 \\ \hline Baseline & 1.0 & 100 & 110 & 0.909 & 11,000 \\ \hline Cavity 4 & 1.2 & 120 & 91.67 & 1.309 & 11,000 \\ \hline Cavity 5 & 1.4 & 140 & 78.57 & 1.782 & 11,000 \\ \hline Cavity 6 & 1.6 & 160 & 68.75 & 2.327 & 11,000 \\ \hline \multicolumn{5}{c}{**(b) Neck—Figure 5b**} \\ \hline
**Designation** & **Scale Factor** & **L\({}_{\text{n}}\) (mm)** & **H\({}_{\text{n}}\) (mm)** & **Neck Ratio (L\({}_{\text{n}}\)/H\({}_{\text{n}}\))** & **A (mm\({}^{\text{2}}\))** \\ \hline Neck 1 & 0.4 & 10 & 12.5 & 0.800 & 125 \\ \hline Neck 2 & 0.6 & 15 & 8.  
the simulation results provided in Figure 5a,b. In Figure 5d, it is seen that the transmission loss of the optimized model is increased about 11.6% compared to the baseline model, but this is less effective compared to the increment observed in Figure 5a,b.