When I vibrate one end of a string, the wave is set up?

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Vibrating one end of a string creates a wave due to the principles of wave propagation and superposition. The discussion highlights the need for reading materials on this topic, particularly regarding the PDE wave equation in one dimension. It mentions that while Fourier Series is touched upon in some texts, more comprehensive resources are desired. Additionally, the concept of standing waves is introduced, explaining that they result from the superposition of two waves traveling in opposite directions. Overall, the conversation seeks to deepen understanding of wave mechanics in strings.
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Does anyone have any reading material on how, when I vibrate one end of a string, the wave is set up? French has a tiny section on Fourier Series, but doesn't delve into it much. Any references to books would also be appreciated.
 
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Do searches for solutions to the PDE wave equation in 1-D. If you are referring to a standing wave, the wave is the superposition of two waves traveling in opposite directions.
 
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