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Physics Question of "Temporal Wavenumbers"

Physics Question of "Temporal Wavenumbers"

Physics Question of "Temporal Wavenumbers"

One of my classes borught up the notion of a "temporal wavenumber", which I'm trying to understand. To me, it sound like the frequency, but asking for more clarification, my instructor provided this reponse:

"Consider a time-space signal. FT wrt time gives omega-domain (omega-space domain, to be more exact). Divide that domain by c, and kw is obtained (this is what I call "temporal" wavenumber).
Now Consider the 3D spatial part of the time-space signal. 3D FT wrt space (x,y,z) gives (conventional) kx, ky, kz wavenumber domain (no divide by c required here). Since we now have all four, kw, kx, ky, kz, I find it useful to refer to kw as the temporal wavenumber and kx,ky,kz as spatial wavenumbers."

Given this, my question is whether or not this statement is true or false: "A temporal wavenumber may be multidimensional" ?

Any help is appreciated for understanding this.

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