Porous Absorber Phase Shift

For sake of idle curiosity--



Question #1-- Given the complex z (surface impedance) data provided by the Multi-Layer Absorber Calculator, is there any way to guestimate the phase shift of the audio reflected by a modeled absorber?



For example, using Allard and Champoux model, doing simple dumb rectangular to polar angle transformation on z:



A 24 inch thick pink fluffy absorber (gfr = 5000) shows impedance phase angle of -46 degrees at 31.25 Hz, gradually rising to an impedance phase angle of -5 degrees at 4 KHz.



A 2 inch thick layer of gfr = 27000, backed by 22 inches of gfr 5000, shows an impedance phase angle "in the ballpark" of -30 degrees all the way from 31.25 Hz to 2 KHz.



However I somehow doubt that the phase shift of the reflected audio would be the same as the impedance phase angle, but haven't a clue. Perhaps it would involve some math operation on the absorber's surface impedance vs the impedance of air? Or perhaps the complex surface impedance by itself provides insufficient data to enable the estimation of the phase shift of reflected audio?



Question #2-- Are there known configurations of passive acoustic devices which perform as allpass filters, or Hilbert transformers?



An allpass filter has a flat frequency response but has a nonlinear phase response.



A Hilbert transformer has a flat frequency response but phase shifts all frequencies (within its passband) by 90 degrees.



Thanks!

Porous Absorber Phase Shift