Fourier: Making Waves - Waves | Sines | Cosines - PhET Interactive Simulations

Fourier: Making Waves

Browser-Compatible Version
Learn more

Fourier: Making Waves simulation

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.

System Requirements

Java via CheerpJ;

Java via CheerpJ simulations run in a browser on most devices.
See full Java via CheerpJ system requirements

Java;

Download the java file using the download button.Java simulations run on most PC, Mac, and Linux systems.
See full legacy system requirements