Fourier: Making Waves

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  • Waves
  • Sines
  • Cosines

Topics

  • Waves
  • Sines
  • Cosines

Description

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.

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.
Version 3.06

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Concept questions for Physics using PhET (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
MC Physics
Wave unit (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Demo
Lab
Physics
Wave clicker questions (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
CQs Physics
Waves: Superposition (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
CQs
Lab
Mathematics
Physics
Wave Representations (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Lab Physics
Fourier Making Waves Game (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS Lab Physics
Wave Modeling and Wave addition (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Lab Physics
Alignment of PhET sims with NGSS This contribution was designed by PhET. Trish Loeblein HS Other Biology
Chemistry
Earth Science
Physics
How do PhET simulations fit in my middle school program? This contribution was designed by PhET. Sarah Borenstein MS Other Biology
Physics
Earth Science
Chemistry
Introduction to Fourier Analysis This contribution was designed by PhET. Sam McKagan, Kathy Perkins and Carl Wieman UG-Intro
UG-Adv
HW Mathematics
Physics
Mapping of PhET and IBDP Physics Jaya Ramchandani HS Other Physics
MS and HS TEK to Sim Alignment Elyse Zimmer MS
HS
Other Chemistry
Biology
Physics
Making use of the Sound Simulations Don Cameron HS Lab Physics

Language Download or Run Tips
Basque All Basque Download Run now Fourier: Uhinak sortzen
Bosnian All Bosanski Download Run now FURIJE-OVA SINTEZA - PRAVLJENJE TALASA
Bulgarian All български Download Run now Фурие: Получаване на вълни
Chinese (Simplified) All 中文 (中国) Download Run now 傅里叶:生成波
Chinese (Traditional) All 中文 (台灣) Download Run now Fourier: Making Waves 傅力葉:與波共舞
Croatian All hrvatski Download Run now Kompozicija valova (Fourierova sinteza)
Danish All Dansk Download Run now Fourir: Bølgefremstilling
Dutch All Nederlands Download Run now Boventonen
Estonian All Eesti Download Run now Fourier: Lainete tekitamine
French All français Download Run now Fourier: Création d'ondes
German All Deutsch Download Run now Wellen zusammensetzen nach FOURIER
Greek All Ελληνικά Download Run now Fourier: Δημιουργία Κυμάτων
Hebrew All עברית Download Run now פוריה: עושים גלים
Hungarian All magyar Download Run now Fourier: hullám-LEGO
Indonesian All Bahasa Indonesia Download Run now Fourier : Mengkontruksi Gelombang
Italian All italiano Download Run now Fourier: Costruire le onde
Japanese All 日本語 Download Run now フーリエ級数展開:波の合成
Khmer All Khmer Download Run now Fourier: ការបង្កើតរលក
Korean All 한국어 Download Run now 푸리에: 파동 생성
Lao All Lao Download Run now ຟູເຍ້: ການເຮັດໃຫ້ຄື້ນຟອງ
Macedonian All македонски Download Run now ФУРИОВА СИНТЕЗА -ПРАВЕЊЕ НА БРАНОВИ
Mongolian All Монгол (Монгол) Download Run now Фурьей: Долгион хийх
Persian All فارسی Download Run now تولید موج ها
Polish All polski Download Run now Fourier: Konstruowanie fal
Portuguese All português Download Run now Séries de Fourier: Fazendo Ondas
Portuguese (Brazil) All português (Brasil) Download Run now Fourier: Criando Ondas
Serbian All Српски Download Run now ФУРИЈЕ-ОВА СИНТЕЗА -ПРАВЉЕЊЕ ТАЛАСА
Slovak All Slovenčina Download Run now Fourier: tvorenie vĺn
Spanish All español Download Run now Fourier: Fabricacion de Ondas
Spanish (Mexico) All español (México) Download Run now Fourier: Fabricacion de Ondas
Spanish (Peru) All español (Perú) Download Run now Fourier: Haciendo Ondas
Turkish All Türkçe Download Run now Fourier: Making Waves
Turkmen All Turkmen Download Run now Furýe: tolkun ýasamak
Vietnamese All Tiếng Việt Download Run now Tổng hợp sóng

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Design Team Third-party Libraries Thanks To
  • Chris Malley (developer)
  • Sam McKagan (lead)
  • Carl Wieman
  • Interviewer: Danielle Harlow
  • Interviewer: Sam McKagan