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I Interpretation of complex wave number

  1. Nov 28, 2017 #1
    Dear forum members,

    I'm wondering about the physical meaning of the imaginary part of a complex wave number (e.g., the context of fluid dynamics or acoustics). It is obvious that

    [tex] w = \hat{w} \mathrm{e}^{i k_z z} [/tex]

    describes an undamped wave if [tex] k_z = \Re(k_z) [/tex] and an evanescent wave if [tex] k_z = \Im(k_z) [/tex].

    If [tex] k_z = \Re(k_z) [/tex] is proportional to the energy of the wave, can I interpret
    [tex] k_z = \Im(k_z) [/tex] as a kind of dissipation/reduction of energy per length z?

    Thanks!
     
  2. jcsd
  3. Nov 28, 2017 #2

    Delta²

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    Gold Member

    ##\Re(K_z)## is proportional to the wavelength of wave and ##\Im(K_z)## as you say , relates to the energy reduction per length z.
     
    Last edited: Nov 28, 2017
  4. Nov 28, 2017 #3

    boneh3ad

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    Science Advisor
    Gold Member

    Or energy increase, in the case of an unstable wave. ##\Im(k_z)## needn't be positive.
     
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