  Acoustic metamaterials are increasingly being considered as a viable
technology for sound insulation. Fractal patterns constitute a potentially
groundbreaking architecture for acoustic metamaterials. We describe in this
work the behaviour of the transmission loss of Hilbert fractal metamaterials
used for sound control purposes. The transmission loss of 3D printed
metamaterials with Hilbert fractal patterns related to configurations from the
zeroth to the fourth order is investigated here using impedance tube tests and
Finite Element models. We evaluate, in particular, the impact of the equivalent
porosity and the relative size of the cavity of the fractal pattern versus the
overall dimensions of the metamaterial unit. We also provide an analytical
formulation that relates the acoustic cavity resonances in the fractal patterns
and the frequencies associated with the maxima of the transmission losses,
providing opportunities to tune the sound insulation properties through control
of the fractal architecture.
