Complex wavenumber, definition

In each case the attenuation of sound can be formally represented by defining a complex wavenumber, where the sound attenuation coefficient is the imaginary part of the wavenumber. The complex wavenumber also leads to the definition of a complex sound speed and a complex dynamic elastic modulus. 

Fig. 2 The experimentally determined potential energy V(), expressed as a wavenumber for convenience, as a function of the angle in the hydrogen-bonded complex H20- HF. The definition of

To meet these requirements we first observe that the wavenumber and the phase are coupled to the angles of the velocity C given by expression (64). In this way the angle of any transmitted EMS wave in medium II can be expressed in terms of the angles ex and (3. In analogy with the classical analysis on total reflection, which includes phase differences [35], we introduce a complex form of the angle ex of an EMS wave. The definitions... 

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