## 4 Results and Discussion
### Double-Leaf Resonant Absorber  
Different combinations of perforated panels and micro-perforated membranes were analyzed, in terms of double-panel, double-membrane, and panel-membrane combinations, in order to achieve better absorbing performance over a wider frequency range and validate the prediction model under more complex conditions (testing the use of the transfer matrix method to calculate the absorption).  
First, a double-panel combination that consisted of panel C (backed by 10 mm cavity) and panel B (backed by 50 mm cavity, close to rigid surface) was studied by experiments and analytic method. As a consequence of the addition of a second PP (Figure 6a), two peaks appeared at 300 Hz (\(\alpha\) = 0.82) and 1320 Hz (\(\alpha\) = 0.98), with predicted absorption coefficients fitting well with the measured results, with only few deviations occurring at the frequency below 300 Hz with a maximum error being 0.16 (at 200 Hz). The agreement of two results indicates the reliability of the prediction method for double-panel combination.  
Figure 5: Comparison of the predicted and measured sound absorption coefficients for: (**a**) different perforated panels with a 20 mm cavity; (**b**) micro-perforated membrane M4 with different cavity depth: 25 mm, 40 mm, 60 mm thick.  
Figure 6: Comparison of the predicted and measured sound absorption coefficients for: (**a**) double-panel structure: perforated panel C followed by a 10 mm cavity combined with panel B followed by a 50 mm cavity, (**b**) perforated panel B followed by a 20 mm cavity combined with M5 followed by a 40 mm cavity.  
The absorption characteristic of one combination consisting of perforated panel (B) and micro-perforated membrane (M5) was investigated in order to check the validity of the prediction model for a combination of microperforated membrane and panel (Figure 6b). Even in this case, the second layer caused a new peak to appear. The measured results were in good agreement with the predictions, as the one-third octave band values reasonably matched the predicted curve.  
For the case of a double-leaf micro-perforated membrane, a combination of samples M4 (surface layer) and M5 both backed by a 25 mm cavity was taken into account (Figure 7a). The predicted sound absorption coefficient showed a sufficient agreement with the measured values, with the most evident difference appearing on the second peak where the absorption was lower than the predicted value by approximately 0.2. In the comparison with individual micro-perforated membrane (M4 and M5), the combined sample showed a much more efficient absorption capability, with two distinct peaks and a broader bandwidth spanning from 420 Hz to 1940 Hz (the absorption values in this range being always over 0.5). This time the absorption coefficients in the \"valley\" between the two peaks were higher, unlike previous cases, in which two layers were combined, confirming that micro-perforated panels behave better than normal perforated panels.  
Finally, the configuration with three layers was investigated to validate the prediction model. In this case, measurements were carried out using both tubes given the extended frequency range of the absorber, thus including frequencies up to 4 kHz one-third octave band. For testing purposes, the following assembly was considered to ensure that the peaks were evenly spaced over a wider range and well identifiable: the outer layer was panel D, followed by a 10 mm air gap, and then micro-perforated membrane M4, 15 mm air gap, micro-perforated membrane M5, and a final 30 mm cavity. The results, as shown in Figure 7b, demonstrated that the agreement between measurements and predictions was generally good, with the largest variations appearing around 400 Hz, where the measured absorption was lower, and around 2 kHz, where measurements outperformed predictions.