# An Integration Strategy for Acoustic Metamaterials to Achieve Absorption by Design
## 6 Comparison with Conventional Acoustic Absorbers  
It has to be emphasized that causal optimality can be attained in conventional acoustic absorbers such as micro-perforated panel (MPP) and acoustic sponge [13]. However, they lack freedom for adjusting the absorption spectrum to a dictated target. Therefore, within the same thickness, although the causal integral Equation (1) can give the same value, the proposed absorption-by-design strategy can concentrate the absorption resources into the frequency region of interest, e.g., the peak region in the noise spectrum, thereby achieving better noise remediation.  
MPP is a well-known conventional resonance absorber, utilizing the acoustic resonance of the back cavity to enhance the dissipation provided by the micro-pores in the front panel. It can achieve relatively high absorption at low frequencies. In the original paper of [PERSON] [14; 15], an MPP comprising a 0.2 mm-thick aluminum plate perforated by 0.2 mm diameter circular holes with an area fraction of 2%, backed by a 6 cm cavity, can display an absorption spectrum as shown by the blue symbols (experiment) and blue line (theory) in Figure 6. The absorption peaks at 640 Hz and rapidly drop away at higher frequencies. In contrast, fiberglass is a commonly used porous material that dissipates sound by the frictions in its porous structures. Its absorption is thereby naturally broadband. A layer of 6-cm thick fiberglass (denoted by green symbols) is noted to have a flat absorption around 90% (10 dB) for frequencies higher than 800 Hz. Compared with the designed metamaterial absorber with the same thickness (5.63-cm metamaterial with 3 mm sponge in front), shown by the red circles (experiment) and line (theory), it is clear that within the target absorption frequency range of above 800 Hz, our designed metamaterial structure is 5 to 10 dB better than the fiberglass. This is achieved precisely by concentrating the absorption resources in the target frequency regime.  
The above comparisons emphasize the point that under the constraint of causality, the absorption-by-design approach can provide an efficient way to utilize the limited absorption resources to achieve the optimal sound attenuation in frequencies of interest. This feature is particularly essential for solving noise problems in mechanical systems like large machines, transformers, and aircraft engines, etc., in which the noise is broadband but with featured spectra.  
Figure 6: Reflection loss (dB) for the 5.93-cm thick designed metamaterial absorber (red curve (theory) and symbols (experiment, measured by using the impedance tube)), the micro-perforated panel (MPP) absorber with 6-cm back chamber (blue curve (theory) and symbols (experiment)), and a layer of 6-cm thick fiberglass (green symbols (experiment)). The blue curve is from [PERSON]’s theoretical model and pentagons are the experimental data from [PERSON]’s original paper [14; 15]. It is seen that the solid red curve is about 3 to 5 dB above the red open circles, which represent the measured results. This difference is due to the fabrication error of not being able to achieve the required (very thin) thickness of the walls separating the FP channels.