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Starting at about maybe 1 megahertz, you'll start to couple signals into adjacent wires. At moderately low powers, like signals in computers, this may be negligible, but at extremely high powers as in a radio transmitter, nearby wires can pick up a lot of power, and in extremely low powers, as in receiving antennas, enough noise can be input or power can be lost to be a problem.
I'd say that at about 100 mHz, even ordinary signals start to need to take the nearby regions into account. You can see this in hard drive cables; as the data speed has risen, the old 40 wire cable has been redesigned into an 80 wire cable where every other wire is a ground.
Also starting around 100 mHz, the sizes of ordinary circuits is close enough to the signal wavelength that resonance and radiation starts to be a problem - this is why SCSI computer cables have terminators.
Up in the gigahertz range, much of the electric signal energy is not so much in the wire as in the region of space near it, that wires begin to be replaced with waveguides, boxes that look like heating ducts that guide the signal energy. But carefully designed coaxial cables are still used up in the 10s of gigahertz ranges.
You would probably have trouble getting anything over 70 GHz onto the wire. Below that, you can probably excite energy to travel down it. How far and how well, that is another question.
Wire has no frequency limitations up to a reasonable frequency, (many GHz.), the property you should be concerned with is impedance, a bare wire in air has a dielectric constant slightly above 1 and would offer a high impedance as would a PVC covered wire, if your source is a low impedance you could expect losses due to the reflection from the impedance mismatch, that's why they invented coax. which is the normal method of delivering an RF signal from point A to point B with minimum loss.
SiGiNT
Or you could just wrap some aluminum foil around it and slide it around until you get the mximum signal out of it. ;-p
I noticed a comment here from a friend and decided to add a further comment both to say hello to him and suggest further refinement of the question about a wire. He knows who I am talking about. Hi Buddy!
A 10 MHz bandwidth signal is starting to get useful as a clarification of your question. That indicates how wide the signal is in frequency but not where in the band it is visible. If it was at 100 MHz (center) the answer would be different than if the signal was at 10 GHz. If it was a "baseband" signal the answer also changes.
You might also see if you have a "return path" in your system. That plays into the mix as well.
We can all continue to play 20 questions and you can continue to get vague answers because the situation you are concerned about is not clear. You have not provided enough detail about your situation and requirements.
My first reaction is that it will probably work. Just try it and you will not have to figure out how to ask a meaningful question. Understanding the situation and using an appropriate can make things significantly better than throwing something together and hoping for the best.
Saying 10 MHz bandwidth without a center frequency designates 0 to 10 Mhz usually. Because 10 cm is considerably below the 10 MHz wavelength of 30 m, you don't have to think about transmission line impedance in this case.
The area spanned between the wire and the return path has an inductance, however (e.g. some 100 nH). If you are intending to use your conductor geometry with high current/low voltage, the inductance probably matters.
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