Impedance function calculation for the study of waves in locally periodic arrangements

Abstract

In this paper, we study theoretically the propagation of waves in locally periodic systems. To this end, we employ a simple method based on the impedance function which is similar to the one used in the transmission line theory. Results are presented for the particular cases of mass-loaded strings arrangements. These systems are easily reproducible in laboratory of introductory and/or advanced courses of physics, and contain all the main characteristics of locally periodic media. Transmission coefficient and normal frequencies are calculated for both mono and diatomic chains, and compared with previously computed and experimental data. Moreover, we show that the corresponding eigenfunctions can be obtained easily from the knowledge of the impedance function.