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## Wave equation
The Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange. The general form of the wave equation is:
c is a fixed constant, the speed of the wave's propagation. For a sound wave in air this is about 300 m/s, and we refer to the speed of sound. For the vibration of string this can vary widely, on a spiral spring (a slinky) it can be as slow as a meter per second.
The basic wave equation is a linear differential equation which means that the amplitude of two waves interacting is simply the sum of the waves. This means also that a behavior of a wave can be analyzed by breaking up the wave into components. The Fourier transform breaks up a wave into sinusodal components and is useful for analyzing the wave equation.
The one-dimensional form can be derived from considering a flexible string, stretched between two points on a
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