Interpretation of complex wave number

[MaAl]

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!

 

[Delta2]

##\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.

 

[boneh3ad]

##\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.

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