Waves in locally periodic media

We review the theory of wave propagation in one dimension through a medium consisting of N identical "cells." Surprisingly, exact closed-form results can be obtained for arbitrary N. Examples include the vibration of weighted strings, the acoustics of corrugated tubes, the optics of photonic crystal s, and, of course, electron wave functions in the quantum theory of solids. As N increases, the band structure characteristic of waves in infinite per iodic media emerges. (C) 2001 American Association of Physics teachers.