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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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Teaching Resources
Main Topics
- Waves
- Sines
- Cosines
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.
Tips for Teachers
The teacher's guide (pdf) contains tips created by the PhET team.
Teaching Ideas
| Title | Authors | Level | Type | Updated |
|---|---|---|---|---|
Concept questions for Physics using PhET (Inquiry Based)
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Trish Loeblein | UG-Intro HS |
CQs | 7/7/13 |
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Wave unit (Inquiry Based)
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Trish Loeblein | UG-Intro HS |
CQs Lab Demo |
7/9/13 |
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Wave clicker questions (Inquiry Based)
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Trish Loeblein | UG-Intro HS |
CQs | 7/9/13 |
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Fourier Making Waves Game (Inquiry Based)
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Trish Loeblein | HS | Lab | 7/7/13 |
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Wave Modeling and Wave addition (Inquiry Based)
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Trish Loeblein | HS UG-Intro |
Lab | 7/7/13 |
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Wave Representations (Inquiry Based)
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Trish Loeblein | HS UG-Intro |
Lab | 7/7/13 |
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Waves: Superposition (Inquiry Based)
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Trish Loeblein | UG-Intro HS |
CQs Lab |
7/9/13 |
| Making use of the Sound Simulations | Don Cameron | HS | Lab | 9/18/07 |
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Introduction to Fourier Analysis
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Sam McKagan, Kathy Perkins and Carl Wieman | UG-Adv UG-Intro |
HW | 4/20/10 |
You can submit your own ideas and activities.
Translated Versions:
| Language | Language (Translated) | Simulation Title | ||
|---|---|---|---|---|
| Basque | Basque | Fourier: Uhinak sortzen | Run Now | |
| Bosnian | Bosnian | FURIJE-OVA SINTEZA - PRAVLJENJE TALASA | Run Now | |
| Brazilian Portuguese | português (Brasil) | Fourier: Criando Ondas | Run Now | |
| Bulgarian | български | Фурие: Получаване на вълни | Run Now | |
| Chinese - Simplified | 中文 (中国) | 傅里叶:生成波 | Run Now | |
| Chinese - Traditional | 中文 (台灣) | Fourier: Making Waves 傅力葉:與波共舞 | Run Now | |
| Croatian | hrvatski | Kompozicija valova (Fourierova sinteza) | Run Now | |
| Danish | Dansk | Fourir: Bølgefremstilling | Run Now | |
| Dutch | Nederlands | Boventonen | Run Now | |
| Estonian | Eesti | Fourier: Lainete tekitamine | Run Now | |
| French | français | Fourier: Création d'ondes | Run Now | |
| German | Deutsch | Wellen zusammensetzen nach FOURIER | Run Now | |
| Greek | Ελληνικά | Fourier: Δημιουργία Κυμάτων | Run Now | |
| Hebrew | עברית | פוריה: עושים גלים | Run Now | |
| Hungarian | magyar | Fourier: hullám-LEGO | Run Now | |
| Indonesian | Bahasa Indonesia | Fourier : Mengkontruksi Gelombang | Run Now | |
| Italian | italiano | Fourier: Costruire le onde | Run Now | |
| Japanese | 日本語 | フーリエ級数展開:波の合成 | Run Now | |
| Khmer | Khmer | Fourier: ការបង្កើតរលក | Run Now | |
| Korean | 한국어 | 푸리에: 파동 생성 | Run Now | |
| Macedonian | македонски | ФУРИОВА СИНТЕЗА -ПРАВЕЊЕ НА БРАНОВИ | Run Now | |
| Persian | Persian | تولید موج ها | Run Now | |
| Polish | polski | Fourier: Konstruowanie fal | Run Now | |
| Portuguese | português | Séries de Fourier: Fazendo Ondas | Run Now | |
| Serbian | Српски | ФУРИЈЕ-ОВА СИНТЕЗА -ПРАВЉЕЊЕ ТАЛАСА | Run Now | |
| Slovak | Slovenčina | Fourier: tvorenie vĺn | Run Now | |
| Spanish | español | Fourier: Fabricacion de Ondas | Run Now | |
| Spanish (Peru) | español (Perú) | Fourier: Haciendo Ondas | Run Now | |
| Turkmen | Turkmen | Furýe: tolkun ýasamak | Run Now | |
| Vietnamese | Tiếng Việt | Tổng hợp sóng | Run Now |
Software Requirements
| Windows | Macintosh | Linux |
|---|---|---|
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Microsoft Windows
XP/Vista/7 Sun Java 1.5.0_15 or later |
OS 10.5 or later
Sun Java 1.5.0_19 or later |
Sun Java 1.5.0_15 or later |
Credits
| Design Team | Third-party Libraries | Thanks To |
|---|---|---|
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