Acoustic wave propagation in a one-dimensional layered system

Propagation of acoustic waves in a one-dimensional water duct containing many air filled blocks is studied by the transfer matrix formalism. Energy distribution and interface vibration of the air blocks are computed. For periodic arrangement, band structure is calculated analytically, whereas the Lyapunov exponent and its variance are computed numerically for random situations. A distinct collective behavior for localized waves is found. The results are also compared with optical situations.