Periodic inclusions create acoustic band gaps via Bragg and Mie mechanisms
Phononic crystals are periodic elastic composites with acoustic band gaps — frequency ranges where sound cannot propagate. Bragg gaps occur at ω ≈ πc/a (half wavelength = lattice constant a). Mie resonance gaps arise when inclusion diameter ≈ wavelength, independent of periodicity. The density-of-states shows the gap, and higher density contrast gives wider gaps. Analogous to photonic crystals for EM waves.