Abstract
The problem of string vibration prompted mathematicians to find a suitable equation to express this phenomenon, which led to the birth of the Fourier series and integrals. The physical law of string vibration can be expressed by wave equation and solved by Fourier series. The study on the wave equation is fraught with mathematical and physical controversy. D.Bernoulli based on results from physical experiments to make a bold conjecture that the shape of a vibrating string can be described as a combination of trigonmetric series, which was inspired and validated by work from Fourier on study on heat equation. This study reviews the wave equation using Fourier as a tool. This paper not only gives the derivation of the wave equation but also explores its solution and corresponding properties.
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