1D Phononic Crystal — Elastic Wave Transmission

Band gaps from periodic impedance mismatch + real-time wave propagation

Unit Cells N N = 8
Impedance Ratio Z₂/Z₁ Z₂/Z₁ = 4.0
Drive Frequency f = 0.40
Layer Thickness d₂/d₁ d₂/d₁ = 1.0

Transfer matrix method: each layer's acoustic transmission is computed exactly. Band gaps (red regions in transmission spectrum) arise from Bragg reflection at the periodicity scale. Top panel: transmission T(f) vs frequency. Bottom: snapshot of wave displacement in crystal. The orange vertical line marks the current drive frequency.