# Fourier: Making Waves

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### 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.

### Esimerkkejä oppimistavoitteista

• 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

 Opettajan opas (pdf) sisältää PhET-tiimin vinkkejä. ( PDF ).

### Teacher-Submitted Activities

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Albania All shqip Analiza Furie: prodhimi i valëve
Amhara All Amharic አራትዮሽ፡ ሞገድ መስራት
Baski All Euskara Fourier: Uhinak sortzen
Bosnia All Bosanski FURIJE-OVA SINTEZA - PRAVLJENJE TALASA
Brasilian portugali All português (Brasil) Fourier: Criando Ondas
Bulgaria All български Фурие: Получаване на вълни
Espanja All español Fourier: Fabricacion de Ondas
Espanja (Meksiko) All español (México) Fourier: Fabricacion de Ondas
Espanja (Peru) All español (Perú) Fourier: Haciendo Ondas
Heprea All עברית פוריה: עושים גלים
Hollanti All Nederlands Boventonen
Indonesia All Bahasa Indonesia Fourier : Mengkontruksi Gelombang
Italia All italiano Fourier: Costruire le onde
Japani All 日本語 フーリエ級数展開:波の合成
Khmer All Khmer Fourier: ការបង្កើតរលក
Kiina - perinteinen All 中文 (台灣) Fourier: Making Waves 傅力葉:與波共舞
Kiina - yksinkertaistettu All 中文 (中国) 傅里叶:生成波
Korea All 한국어 푸리에: 파동 생성
Kreikka All Ελληνικά Fourier: Δημιουργία Κυμάτων
Kroatia All hrvatski Kompozicija valova (Fourierova sinteza)
Lao All Lao ຟູເຍ້: ການເຮັດໃຫ້ຄື້ນຟອງ
Makedonia All македонски ФУРИОВА СИНТЕЗА -ПРАВЕЊЕ НА БРАНОВИ
Mongoli All Монгол (Монгол) Фурьей: Долгион хийх
Persia All فارسی تولید موج ها
Portugali All português Séries de Fourier: Fazendo Ondas
Puola All polski Fourier: Konstruowanie fal
Ranska All français Fourier: Création d'ondes
Saksa All Deutsch Wellen zusammensetzen nach FOURIER
Serbia All Српски ФУРИЈЕ-ОВА СИНТЕЗА -ПРАВЉЕЊЕ ТАЛАСА
Slovakki All Slovenčina Fourier: tvorenie vĺn
Tanska All Dansk Fourir: Bølgefremstilling
Turkki All Türkçe Fourier Serileri: Dalga Yapalım
Turkmeeni All Turkmen Furýe: tolkun ýasamak
Unkari All magyar Fourier: hullám-LEGO
Vietnam All Tiếng Việt Tổng hợp sóng
Viro All Eesti Fourier: Lainete tekitamine
Windows Macintosh Linux
Microsoft Windows
XP/Vista/7/8.1/10