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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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Version 3.04
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Topics Teaching Ideas Software Requirements Translated Versions Credits

Topics

Main Topics

  • Waves
  • Sines
  • Cosines

Related Topics

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.

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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.

Ascending Sort (Z-A)Title Author Level Type Updated
Concept questions for Physics using PhET (Inquiry Based) Designed by PhET IconImage of Gold StarT. LoebleinUG-Intro
HS		CQs8/09
Fourier Making Waves Game (Inquiry Based) Designed by PhET IconImage of Gold StarT. LoebleinHSLab11/08
Introduction to Fourier Analysis Designed by PhET IconS. McKaganUG-Intro
UG-Adv		HW7/08
Making use of the Sound Simulations D. CameronHSLab9/07
Wave clicker questions (Inquiry Based) Designed by PhET IconT. LoebleinHS
UG-Intro		CQs11/08
Wave Modeling and Wave addition (Inquiry Based) Designed by PhET IconT. LoebleinUG-Intro
HS		Lab11/08
Wave Representations (Inquiry Based) Designed by PhET IconImage of Gold StarT. LoebleinUG-Intro
HS		Lab11/08
Wave unit (Inquiry Based) Designed by PhET IconImage of Gold StarT. LoebleinUG-Intro
HS		CQs
Lab
Demo		8/09
Waves: Superposition (Inquiry Based) Designed by PhET IconImage of Gold StarT. LoebleinUG-Intro
HS		CQs
Lab		11/08

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Software Requirements

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Windows Systems Macintosh Systems Linux Systems
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

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Translated Versions

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Credits

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