A Study on the Generation and Propagation of Traveling Waves in Strings

Abstract

Traveling and standing waves occurring in mechanical systems are the results of the interplay of excitation sources, locations, and boundary conditions. While traveling waves carry energy throughout a system, standing waves keep such energy within a located area associated with the modes of excitation. Depending on the desired characteristics of a system, it is crucial to understand the wave propagation and what parameters affect wave propagations. In the present work, one-dimensional string equations are studied with fixed-fixed boundary condition with the purpose of generating steady-state traveling waves. Two excitation forces at various frequencies of excitation are applied to a string near opposing boundaries to understand the generation and propagation of traveling and standing waves. The work focuses on how parameters affect the wave propagation on a string under the fixed-fixed boundary condition and their quality examined. Understanding the effects of these parameters on the wave propagation of a string can lead to better understanding of microorganism behaviors, such as the propulsion of flagella or biological counter parts such as the basilar membrane (2D string) in the ear’s cochlea that exhibit non-reflective waves.