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\pagestyle{empty}\begin{document}\title{}\author{David J.C. MacKay }\date{}
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Computational Methods in Physics
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\section*{Dispersive Waves}
Simulate the progress of a wave packet along a long thin wave tank
containing `deep' water. Make an initial condition (a Gaussian
shaped impulse, for example) and take its Fourier transform so as to
represent it as a superposition of travelling waves of all frequencies.
Obtain the state at subsequent times by propagating each wave at its
phase velocity, given by the known dispersion relation, and adding up
the sinusoidal waves again.
Give a quantitative translation of your simulation using the known
density of water and the value of $g$.
Does your simulation give a wavepacket with the expected properties
(group velocity, dispersion, energy)?
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\hfill DJCM \today
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