National Science Foundation
Excellence Center of Science and Mathematics Education at King Saud University
Fourier: Making Waves
Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.
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Topics
Main Topics
- Waves
- Sines
- Cosines
Related Topics
- Quantum Mechanics, Harmonic motion, Wavelength, Amplitude, Frequency, Fourier Series, Fourier Analysis, Superposition, Period, Uncertainty Principle, Wave Packets
Sample Learning Goals
- Explain qualitatively how sines and cosines add up to produce arbitrary periodic functions.
- Recognize that each fourier component corresponds to a sinusoidal wave with a different wavelength or period.
- Mentally map simple functions between Fourier space and real space.
- Describe sounds in terms of sinusoidal waves.
- Describe the difference between waves in space and waves in time.
- Recognize that wavelength and period do not correspond to specific points on the graph but indicate the length/time between two consecutive troughs, peaks, or any other corresponding points.
- Become comfortable with various mathematical notations for writing Fourier transforms, and relate the mathematics to an intuitive picture of wave forms.
- Determine which aspect of a graph of a wave is described by each of the symbols lambda, T, k, omega, and n.
- Recognize that lambda & T and k & omega are analogous, but not the same.
- Translate an equation from summation notation to extended notation.
- Recognize that the width of a wave packet in position space is inversely related to the width of a wave packet in Fourier space.
- Explain how the Heisenberg Uncertainty principle results from the properties of waves.
- Recognize that the spacing between Fourier components is inversely related to the spacing between wave packets, and that a continuous distribution of fourier components leads to a single wave packet.
Teaching Ideas
Tips for Teachers
The teacher's guide contains tips for teachers created by the PhET team (PDF).
Ideas and Activities for this Sim
There are 9 contributions listed.
 Title | Author | Level | Type | Updated |
Concept questions for Physics using PhET (Inquiry Based)   | T. Loeblein | UG-Intro HS | CQs | 8/09 |
| Fourier Making Waves Game (Inquiry Based) | T. Loeblein | HS | Lab | 11/08 |
| Introduction to Fourier Analysis | S. McKagan | UG-Intro UG-Adv | HW | 7/08 |
| Making use of the Sound Simulations | D. Cameron | HS | Lab | 9/07 |
| Wave clicker questions (Inquiry Based) | T. Loeblein | HS UG-Intro | CQs | 11/08 |
| Wave Modeling and Wave addition (Inquiry Based) | T. Loeblein | UG-Intro HS | Lab | 11/08 |
| Wave Representations (Inquiry Based) | T. Loeblein | UG-Intro HS | Lab | 11/08 |
| Wave unit (Inquiry Based) | T. Loeblein | UG-Intro HS | CQs Lab Demo | 8/09 |
| Waves: Superposition (Inquiry Based) | T. Loeblein | UG-Intro HS | CQs Lab | 11/08 |
Submit Your Ideas & Activities
Software Requirements
| Windows Systems | Macintosh Systems | Linux Systems |
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Microsoft Windows XP/Vista/7 Sun Java 1.5.0_15 or later |
OS 10.4.11 or later Apple Java 1.5.0_19 or later |
Sun Java 1.5.0_15 or later |
Translated Versions
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Credits
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