I Understanding Waves: The Importance of Fourier Analysis in Undergraduate Physics

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Understanding Fourier analysis is essential for studying waves at an undergraduate level, particularly in junior and senior courses. While it may not be crucial for introductory physics, it provides valuable insights into harmonics for those interested in the topic. Learning Fourier theory early can enhance comprehension of wave phenomena. The Fourier transform is noted for its broader applicability in various fields. A solid grasp of this mathematical tool will ultimately benefit students in their physics studies.
kent davidge
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if I am to learn about waves at an undergraduated level, how much is it important to learn Fourier theory before I actually go into the physics?
 
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Well, it depends on what will you study, but you will need it someday so I would recommend you to learn it as soon as possible.
 
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The Fourier transform is probably more generally useful anyway.
 
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kent davidge said:
if I am to learn about waves at an undergraduated level, how much is it important to learn Fourier theory before I actually go into the physics?
If it's introductory physics then it's not that important, unless you are attracted to the topic, then it can give you some insight as to what's going on when you study harmonics. On the other hand, if you are studying waves at the junior or senior level, you will find an understanding of Fourier analysis very helpful.
 
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Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
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