Learning Goals
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- 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.
- Describe sounds in terms of sinusoidal waves.
- Compare and contrast 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.
- Relate the mathematical notation of a Fourier series to its graphical representation and determine which aspect of the graph is described by each of the symbols in the equation.
- Recognize that λ & T and k & ω are analogous, but not the same.
- Translate an equation from summation notation to expanded 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.