Phononic Crystal
A 1D phononic crystal is a periodic array of alternating elastic materials. Bragg scattering at each interface causes destructive interference at certain frequencies — creating bandgaps where waves cannot propagate.
cos(kd) = cos(k₁d₁)cos(k₂d₂)
− ½(Z₁/Z₂+Z₂/Z₁)sin(k₁d₁)sin(k₂d₂)
Z = ρc (acoustic impedance)
− ½(Z₁/Z₂+Z₂/Z₁)sin(k₁d₁)sin(k₂d₂)
Z = ρc (acoustic impedance)
Controls
Band Info
PASS
Wave state
1.00
Transmission
—
1st gap low
—
1st gap high
Top: Wave displacement through the crystal — watch amplitude decay in bandgap. Bottom: Dispersion relation (band structure). Red line = current frequency.