Is Fourier Analysis Useful for High School Students?

[Titan97]

Is learning Fourier analysis useful for a high school student? If so, which book should I refer for learning the basics of Fourier analysis? This topic is not in my syllabus. But will it be useful for solving problems? (even if its not, it seems interesting to me).
I have learned single variable calculus.

 

[micromass]

Whether it is useful or not depends on your goals. Whether it is useful for solving problems depends on the problems.

 

[axmls]

What micromass said. That said, Fourier analysis can be quite beautiful and its physical consequences are fascinating. Perhaps a short introduction and overview of what Fourier analysis is about would be interesting to you, but save the full treatment for when you're more mathematically able.

 

[micromass]

Fourier analysis can be quite beautiful and its physical consequences are fascinating.

Oh, most definitely. I guess many physics and engineering majors learn about Fourier analysis when solving applications. But as a mathematics major, I learned about Fourier analysis in a very sterile pure math context, with no eye for applications whatsoever. It was still extremely beautiful: it's amazing what kind of pure math one can do with Fourier stuff. But seeing the application of Fourier analysis in quantum mechanics was a real eye-opener to me. I think that's one of the most beautiful things I've ever seen. From then on, I really hated the idea of separating pure math from its applications.

 

[Dr. Courtney]

Fourier analysis can be a valuable tool in the toolbox. I mentored an elementary school science project last year where the student used the Fourier transform feature in Audacity to measure the frequency of a guitar note played at different temperatures to test a hypothesis regarding frequency vs. temperature. I also worked with a high school student on a project demonstrating accuracy advantages of computing Fourier transforms by explicit integration instead of fast Fourier transform methods. The student is now beginning work on using the more accurate Fourier transform on environmental applications.

Fourier analysis will provide a tool in your tookbox that very few high school and early college students have, which may be an advantage if you want to land a job in a college lab or other research environment. Applications can pop up in many areas of science and engineering, but without the tool in your toolbox, you might not think of it.

Here are links to a few of our papers. A couple are introductory and educational:

http://arxiv.org/ftp/physics/papers/0605/0605154.pdf

http://arxiv.org/ftp/arxiv/papers/1211/1211.4832.pdf

http://arxiv.org/pdf/1507.01832v1.pdf

It is surprising how much you can do and learn with a few musical instruments and Audacity.

Download our Fourier transform program (link in my sig) and you can do even more. Oscillatory data sets are widely available all over the net: temperatures, tides, sounds, greenhouse gas concentrations, etc.