Unformatted text preview: amplitude spectrum ˜ f f ( y ) = 1 √ 2 π Z ∞∞ dk ˜ f ( k ) exp( ı k y ) ˜ f ( k ) = 1 √ 2 π Z ∞∞ dy f ( y ) exp(ı k y ) The integral transformation that links f and ˜ f is called ²ourier transformation. Solve the lowamplitude acoustic wave equation for a sound speed that depends on the frequency ω or wavenumber k . Can I still write the solution as a ²ourier integral depending on y = x ± c s t ? The wave packets f and g now consist of waves that propagate with di±erent phase velocities ω/k . Assume a wave packet that contains only waves with frequencies close to ω and that the frequency is a weak function of k , so we may write ω ( k ) ’ ω + d ω d k ± ± ± ± ( kk ) + . . . Calculate the propagation velocity of the wave packet, called the group velocity....
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 Fall '08
 RABE
 Physics, Work, Fundamental physics concepts, phase velocity, acoustic wave equation, lowamplitude acoustic wave

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