APPLICATION OF FOURIER SERIES EXPANSION TO THE STUDY OF SINE SINUSOIDAL WAVE TRAVELLING IN THE POSITIVE X – DIRECTION
Abstract
The phenomena of periodic functions occur quite frequently in mathematics, physics and engineering applications. Therefore, it is an important practical problem to represent the corresponding periodic functions in terms of simple periodic functions such as sine and cosine. In this work, we consider the Fourier series expansion of a trigonometric cosine sinusoidal periodic function: y(x,t) = a sin(kx - ωt - ε), which is acting within the permitted region of space: -π < x < π. The periodic function could be the description of motion of ame particle of mass m with energy E moving under the influence of some finite potential field V. This work talks about the spectrum of unmodulated periodic functions where we use the Fourier series expansion to obtain mathematical answers and thereby using excel to obtain final result. It is revealed in this study, that within the classically allowed region of space, the Fourier series solution of the cosine periodic function are real and non- degenerate, and the approximate wave function is oscillatory with decreasing amplitudes as the frequency mode n becomes very large.
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