This Java Applet displays the sum of harmonic waves. The user may select relative amplitudes (magnitude in the simulation) and phases of the terms in the Fourier series. There are buttons to display several typical functions and their corresponding series (Sine, Triangle, Sawtooth, and Square) as well as various signal modifications/degradations to those wave forms. Sliders are used to control amplitude and phase. The user may also select the number of Fourier terms to add up, a first harmonic frequency, and select play the resultant sound.
Type of Material:
Java Applet simulator
This material is well suited for individual investigation, classroom demonstration, or as a building block for an assignment.
Java enabled browser.
Identify Major Learning Goals:
Develop a facility for understanding Fourier series of common wave-forms and various types of signal modifications.
Target Student Population:
Undergraduate physics majors. Students taking electronics, quantum mechanics, classical mechanics, or other courses covering Fourier Analysis/Synthesis.
Prerequisite Knowledge or Skills:
The user should have some idea of superposition of wave forms and a sense of what adding different frequency components means.
The quality of the content is excellent. The calculations appear accurate. There are several different visualizations of the frequency components.The display panel opens up with a square-wave function and the corresponding Fourier series summation for a number of terms. A user can immediately start playing with features and examine effects of changing amplitude or phase of the various terms. Also the user can change the number of terms, or draw their own function and see the corresponding series.
The control of amplitude and phase are through sliders. This gives the user limited quantitative control. Since the display does not have measuring tools, the user is only able to view the material in a qualitative manner.
Potential Effectiveness as a Teaching Tool
Users will be able to get a clear concept of what is involved in Fourier analysis without the need to get bogged down in any abstract mathematics. This provides a simple way to present Fourier concepts also without the need for programming, or use of scientific graphing programs, or spreadsheet numerical analysis. The results are simply displayed. The variety of graphical ways to see the frequency components and the various wave-form modifiers (e.g. clipping, rectification, etc) allow one to not only see how the different frequency components fit together, but also how various common wave-form modifications affect the resulting waves. The audio output of the wave form is a particularly nice touch.
The learning should not be limited to what is presented in this simulation. To study the topic completely a student will need a more complete theoretical and numerical introduction to Fourier series. Instructors will need to have specific exercises, demonstrations, or activities planned for this item. The applet help only gives information on the operation of the applet.
Ease of Use for Both Students and Faculty
The module operates as intended. The interface is reasonably easy to use and navigate considering its sophistication. The means of changing key features (magnitudes, amplitudes, phases) is very easy and intuitive. Other features have descriptions on the Full Directions web page.
The item displays three cycles of the periodic function. This does not appear to be user selectable.
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