Fig. 4: The experimental realization of duality-symmetric sample.

a The schematic of coupled Helmholtz resonators (CHR). The color indicates the total pressure mode at maximal absorption frequency. The thickness \(L=2.5{{\rm{cm}}}\). b The fabricated sample (half model) filled with porous foam. c The monopole and dipole modes at 2500 Hz (pressure field). d The corresponding scattering strength spectra of CHR. e The scattering spectra of CHR (transmission, reflection, and absorption). f The ratio between absorption integral \(\gamma (\omega )\) and \(\Gamma\). g The extracted effective density and h effective compressibility. The black lines represent the results by the modified surrogate model, the colored lines are simulation data, and the circles are measured data by the impedance tube measurement.