# Fourier: Making Waves

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• شه‌پۆله‌کان
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• کۆسینوس

### 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

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

### Teacher-Submitted Activities

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