Wave propagation analysis in spiral geometries

Abstract

In this paper wave propagation in strings of exponential and conical spiral geometries and in an exponential spiral horn of increasing circular cross-section area is studied. The three-dimensional wave equation in cylindrical coordinates is investigated, as the theoretical solution in the exponential spiral horn is derived and in the case of the strings, numerical simulation mainly using a centered in time and space finite difference scheme is carried out. The results suggest non-harmonic resonance modes in both of the conical and exponential spiral strings.