Solving Partial Differential Equations for Wave Equation Problem on Strings by Applying the Fourier Transform

Amelia; Endang  Rusyaman; Dianne Amor  Kusuma; Azril

doi:10.24036/eksakta/vol23-iss04/346

EKSAKTA: Berkala Ilmiah Bidang MIPA

Open Access

Solving Partial Differential Equations for Wave Equation Problem on Strings by Applying the Fourier Transform

Amelia ¹

, Endang Rusyaman ¹

, Dianne Amor Kusuma ¹

, Azril ²

¹ Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia

² Department of Biomedical Engineering, National Cheng Kung University, Tainan City, Taiwan

Published 2023-12-30

Vol. 24 No. 04 (2023) PAGES 574-587

DOI 10.24036/eksakta/vol23-iss04/346

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Abstract

The wave equation on a string is an example of a partial differential equation problem. There are several methods for finding the solution to the wave equation on a string. The solution method will differ depending on definition of the function's domain. This study aims to determine the form of solving the wave equation on the strings and the results of the analysis of the wave motion that depends on the number of boundary conditions, using a particular solution method, namely the Fourier transform method. The boundary conditions used are Dirichlet boundary conditions. The Fourier transform method is used to obtain the solution of the wave equation on the string. The Fourier transform will transform the wave equation on the string and get the solution form of the wave equation on the string by applying the inverse Fourier transform. The results of this study obtained the same form of solution for each state from the wave equation on strings, namely in the form of the D'Alembert solution for the wave equation. As well, the movement of the wave will form a periodic solution by period , with a different form of deviation occurring at each point Â for each value .

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