String Standing WavesFor an ideal string of length L which is fixed at both ends, the solutions to the wave equation can take the form of standing waves: This kind of solution can be verified by direct substitution into the wave equation: Substituting: These two expressions are equal for all values of x and t provided

Index Wave concepts  
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Fourier SeriesIf a continuous function f(t) is periodic with period T, then it may be approximated arbitrarily well by a Fourier series where the coefficients are given by: 
Index Wave concepts 
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