## 3 Results  
### Acquisition of Model  
Figure 10 displays normalized specific acoustic reactance curves for the full set of twenty-five plates (Table 1) for which results were obtained using CFD simulation. All four sub-figures demonstrate that the acoustic reactance curves shift to lower frequencies as the distance between individual holes within a perforated plate decreases. According to Equation (1), these reductions in resonance frequencies imply that the end correction length increases with the decreasing hole separation distance. This is contrary to Fok's function [8], which suggests that hole interaction effect reduces the overall acoustic end correction length, as given in Equation (4). The acoustic velocity magnitude in the vicinity of the perforations is visualized using the results from the CFD simulations of Plate No. 7 with distantly spaced holes, shown in Figure 11, and Plate No. 2 with closely spaced holes, shown in Figure 12. Figure 13 presents a cross-section view of the same holes. There is a clear indication that when holes are distant from each other, such as those on Plate No. 7 absorber, the oscillating masses for each orifice are so far apart that they barely affect each other. The holes radiate pressure fluctuations separately. By contrast, for plate No. 2, the acoustic velocity does not diminish so rapidly when neighboring holes are very close, due to the combined momentum of the interacting jet flows from neighboring holes. As a result, the strong oscillating mass is sustained further downstream and forms an extra film of what may be considered to be high acoustic velocity, as shown in Figure 12. This gives rise to the extra acoustic radiation effect from the perforation area as a whole to the acoustic downstream space. In this paper, this extra radiation effect is named \"acoustic radiation effect due to the overall perforation area\". Figure 10: CFD obtained resonance frequencies of perforated plate No. 1–25 absorbers (as listed in Table 1). From the other perspective, a close hole separation distance (x/d = 1.5) in Plate No. 2 makes the \"attached mass\" near each individual hole slightly horizontally narrower in comparison with that observed in Plate No. 7 due to hole interaction effect, yet the \"attached mass\" near each individual hole is somewhat stretched in the vertical direction. However, the \"attached mass\" near each individual hole can be considered to not be affected to a noticeable degree by acoustic radiations due to the overall perforation area. Therefore, it may be considered that the end correction due to acoustic radiation for an individual hole is not affected by the acoustic radiation effect, due to the overall perforation area. The acoustic radiation effect from the perforation area as a whole manifests itself by forming an extra acoustic radiation effect in the vicinity of the overall perforated area. The acoustic radiation effect of a perforated plate is treated as a superimposition of two radiation effects: the \"individual hole radiation effect\" and the \"overall perforation region radiation effect\". An acoustic signal experiences the single hole radiation effect and the perforation region radiation effect simultaneously. A simple model is proposed in this paper by assuming that acoustic end correction lengths caused by these effects are additive. Figure 11: Acoustic velocity magnitude contour near perforated plate No. 7 absorber. Figure 12: Acoustic velocity magnitude contour near perforated plate No. 2 absorber. As was introduced earlier, the end correction length due to single hole radiation effect has been analytically derived to be [4; 5; 6]:  
\[l_{sh}=0.96\sqrt{A_{0}} \tag{13}\]  
Consider an extreme case where all perforations are just next to each other (x/d=1). The orifices nearly work as a single large hole in terms of acoustic radiations. Therefore, it is proposed that acoustic end corrections due to the overall perforation area follow a similar form with that caused by an individual hole.