Elastic wave band gaps from periodic mass-spring contrast
A 1D diatomic phononic crystal (alternating masses m₁, m₂ connected by springs k₁, k₂) exhibits acoustic and optical branches separated by a band gap. The gap opens at the Brillouin zone boundary k = π/a due to Bragg scattering. The band gap width grows with mass and spring constant contrast, which is the design principle for acoustic metamaterials and vibration isolators.