Elastic wave propagation through periodic 1D medium — Bragg stop bands
Transmission: — | —
A phononic crystal is a periodic elastic structure with alternating impedance Z = ρc.
Bragg scattering creates band gaps at frequencies f_n = nc/(2a) where constructive
interference of reflected waves leads to exponential attenuation — the stop band.
Left: wave propagation (real part of displacement). Right: band structure dispersion ω(k).