## 5 Discussion
Unbacked MCP1 provides similar a performance between 400 Hz and 700 Hz with, however, lower constant absorption values (between 0.9 and 0.97) above 700 Hz, whereas they exceed 0.97 with the enhanced metamaterial with a  
Figure 12: (**a**) Absorption properties of unbacked MCP1 (plain red), MCP1 backed by a 55 mm cavity depth (dashed red) and a rigidly backed 200 mm anechoic cone of melamine foam (orange, reproduced from Figure 2 in [11]); (**b**) Absorption properties of unbacked MCP1 (plain red), a 110.6 mm depth metamaterial composed of a parallel array of 4 \(\times\) 4 quarter-wavelength coiled resonators (blue with circles, reproduced from Figure 2 in [5]) and the same metamaterial covered by a 10 mm sponge (dashed blue, reproduced from Figure 2 in [5]); (**c**) Absorption properties of unbacked MCP1 (plain red), MCP1 backed by a 35 mm cavity depth (dashed red) and an MPP connected to hollow tubes of variable length in a rigid backing cavity with a depth of 36 mm (green circles, reproduced from Figure 17 in [6]); all the curves are obtained from impedance tube measurements. bandwidth-to-thickness ratio of \(\left.\Delta\lambda/\overline{D}\right|_{120.6}=9.2\). Between 80 Hz and 250 Hz, unbacked MCP1 clearly overcomes the drop in absorption observed with the enhanced metamaterial. Figure 12c compares the absorption performance of a 36 mm MCP1 resonator to that due to an MPP (1 mm thick, perforation ratio 3.9%) connected to flexible hollow tubes of two variable lengths (10 mm and 20 mm), located above a partitioned 35 mm rigid cavity [6], a so-called MPP-T. The MCP1 resonator is efficient over a much broader frequency range with a half-bandwidth of 1560 Hz, instead being 330 Hz for MPP-T, with almost a constant absorption value of 0.88 above 1 kHz, whereas the MPP-T reaches near-unit absorption at 870 Hz and 1460 Hz. At low frequencies below 760 Hz, the MCP1 resonator provides a greater amount of absorption compared to the MPP-T (by up to 40%) due to its broad bandwidth. If used as a liner in aeronautical applications, MCP1 would therefore be better suited to mitigate broadband noise components, whereas the MPP-T is designed to target specific tonal components. The downside of the above-mentioned rigidly backed absorbers (such as the MCP1 absorber, the cone anechoic termination or the enhanced metamaterial) is their drop in performance as the frequency decreases due to the increased stiffness of the air cavity. A solution would be either to use an unbacked MCP1, which does not necessarily provide the best performance above 700 Hz, or a parallel arrangement between MCP1s, in which part of it would be backed by a shallow cavity (with a depth of 10 mm to bring a near-constant absorption of 0.85 over 2-6.5 kHz; see Figure 10), and part of it would be unbacked (to bring a similar amount of absorption over 100 Hz-2 kHz; see Figure 5). A more robust structural design would be to load the latter part by a shallow open cavity of the same depth as the rigid one. The ultra-broadband performance of this sub-wavelength parallel MCP absorber works according to two resonant mechanisms: the first half- (resp. quarter-) wavelength resonance for the open (resp. closed) backing cavity contributes to achieving high particle velocities through the micro-channels of MCP1. An optimization study would then be required to ensure perfect continuity and low overlap between the absorption performance of the individual resonators.