"Variable" is singular, but you have given it a plural verb - are. What are you trying to say? It would be very helpful if you could give us a couple of sentences before the example, so as to give the sentence some context.
The 'the' is optional: with 'the', variables refer to the previously mentioned variables; without the, variables relate to all variables (limited by the context). As you see, both referents are the same.
PS, did you mean
"k is referred to the free-space wavenumber."
"k relates to to the free-space wavenumber."
"k isrefers to the free-space wavenumber." ?