## 5 Discussion
This is the case for MCP1 because Sh < 0.73 up to \(f_{\text{cut-on}}\), unlike the UMPP, for which Sh > 1 above 200 Hz. This explains the reduced efficiency bandwidth for the UMPP with respect to MCP1. Moreover, visco-thermal dissipation essentially occurs within the parallel micro-channels of MCP1 due to its high aspect ratio of 37:1. Conversely, significant contributions to the viscous dissipation arise from vortex shedding at the inlet/outlet of the apertures of the UMPP with high acoustic flow distortion induced by a large hole pitch. Regarding rigidly backed absorbers, the index \(\overline{\alpha}\)\(\Delta\lambda/\overline{D}\) is well suited. Table 3 shows that, regardless of the cavity depth, the MCP1 resonant absorber has the highest acoustic \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & \(\overline{\alpha}_{\text{unb.}}\) & \(\Delta\lambda/\overline{D}\big{|}_{\text{unb.}}\) & \(\overline{\alpha}_{\text{55}}\) & \(\Delta\lambda/\overline{D}\big{|}_{\text{55}}\) & \(\overline{\alpha}_{\text{20}}\) & \(\Delta\lambda/\overline{D}\big{|}_{\text{20}}\) \\ \hline MCP1 & **0.84** & **4150** & **0.71** & **6** & **0.75** & **8** \\ MCP2 & 0.58 & 26 & 0.45 & – & – & – \\ UMPP & **0.55** & **7890** & 0.51 & 5.5 & 0.54 & 7.6 \\ MPP & 0.47 & – & 0.42 & – & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of materials’ absorption performance. efficiency index amongst the materials, followed by the UMPP resonant absorber. As the cavity depth decreases, the bandwidth-to-thickness ratio, \(\Delta\lambda/\overline{D}\), increases toward the ultimate one (24.5). Assessing how the MCP absorbers perform with respect to the existent solutions would be of interest. A comparison is shown in Figure 12 between the performance of MCP1 absorbers as well as state-of-the-art broadband absorbers such as an anechoic termination composed of melamine foam [11] (Figure 12a), a metamaterial composed of a parallel array of coiled resonators, eventually covered by a sponge [5] (Figure 12b) and a rigidly backed MPP connected to hollow flexible tubes inserted into a rigid cavity [6] (Figure 12c). It can be seen from Figure 12a that unbacked MCP1 offers a solution for ultra-short low-frequency anechoic terminations for Kundt tube measurements, up to 2 kHz, complementary to current anechoic terminations composed of a 200 mm cone of melamine foam backed by a rigid end cap. Above 2 kHz, the melamine cone offers better absorption (0.96 at 4 kHz) than unbacked MCP1 (0.77 at 4 kHz) but has a lower bandwidth-to-thickness ratio \(\Delta\lambda/\overline{D}\big{|}_{200}=1.28\) and becomes reflective at low frequencies, with the absorption decaying from 0.7 toward zero below 400 Hz [11]. Instead, unbacked MCP1 produces a controllable amount of near-constant absorption above 0.87 over an ultra-broad bandwidth, typically 100 Hz-2 kHz. Figure 12a also shows that a rigidly backed MCP1 with \(\Delta\lambda/\overline{D}\big{|}_{55}=6\) exceeds the absorption of the anechoic termination by up to 15% between 600 Hz and 2 kHz but produces lower absorption below 600 Hz. Hence, another potential application of an MCP1 resonant absorber could be reducing the noise generated by fuel-efficient ultra-high bypass ratio turbofan engines in aeronautical transport with a targeted bandwidth of 600 Hz-2 kHz [21]. This would, however, require a specific study under grazing sound incidence in the presence of flow. Figure 12b shows that unbacked MCP1 provides a better (resp. almost comparable) absorption performance below (resp. above) 250 Hz with respect to a metamaterial with a thickness of 110.6 mm composed of a parallel array of coiled quarter-wavelength cavity resonators [5] whose individual anti-resonances generate several absorption dips. Covering the metamaterial cavity mouths with a suitable amount of resistive porous material smooths out the absorption dips and provides a near-constant absorption that is greater than 0.9 over a broad bandwidth of 400-1370 Hz [5].