Figure 3

Overview of the TMM prediction of a FMAA behavior mounted in a rectangular section duct of height \(H=15\) cm and such that HR\(_1\) is optimized for \(\alpha ^+(700~{\mathrm {Hz}})=1\) with \(k_0(700~{\mathrm {Hz}})\delta \in ~]0; \pi [\) and with a perfect soft wall at a distance \(\delta \). (a) \(\alpha ^+(f)\) of optimized FMAA for \(k_0(700 {\mathrm {Hz}})\delta \) \(= \pi /2\) and for \(k_0(700 {\mathrm {Hz}})\delta \) \(= \pi /25\). (b) Optimized HR\(_1\) cavity height, \(h_c\), and neck width, \(w_n\). (c) Optimized HR\(_1\) behavior in terms of normalized leakage quality factor, \(Q_{leak}\), and in terms of normalized surface impedance, \(Z_1/S_1\). The dot and triangle maker on the abscissa axis of (b) and (c) indicate that \(k_0(700~{\mathrm {Hz}})\delta \) is equal to \(\pi /25\) and \(\pi /2\), respectively.