Low-frequency dispersion of phonons in one-dimensional chains

The wave velocity of long-wavelength acoustic phonons is found in one-dimensional crystals with an arbitrary basis by an elementary argument founded upon the equality of kinetic and potential energies in a linear wave. This argument also extends to quasiperiodic crystals such as those based on the Fibonacci sequence. Inspired by recent experiments, these ideas are then applied to an artificial quasicrystalline transmission line made by coupling electromagnetic cavities in a Fibonacci sequence.