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

Abstract

The goal of this work is to understand the generation and propagation of one-dimensional steady state traveling waves in a finite medium with a two-force excitation methodology. The solution to the second order partial differential equation describing the equation of motion for a string is theoretically solved considering a fixed-fixed boundary condition. The parameters that affect the generation and propagation of waves should be well understood to control and manipulate the desired system’s response. The string equation is solved by rearranging it based on linear wave components and phase difference components needed to generate steady-state traveling waves in a string. Two excitation forces are applied to a string near the boundaries to understand the generation and propagation of traveling waves at various frequencies. Determining the quality of the traveling waves and understanding the parameters on the wave propagation of a string can lead to further understand and leverage various engineering disciplines such as mechanical actuation mechanisms, propulsion of flagella, and the basilar membrane in the ear’s cochlea.