Does the transmission medium affect the speed of a signal? For instance does light traveling through a fiber cable get a bit from A => B faster than copper can transmit a bit the over the same distance?
Well, definitely yes, i think. Depending on properties of the cable as well as the Relative permittivity(also measured as dielectric constant) of the material surrounding the copper is a factor.
EDIT: The velocity factor also called wave propagation speed or velocity of propagation (VoP or vP), of a transmission medium is the speed at which a wavefront (of an acoustic signal, for example, or an electromagnetic signal, a radio signal, a light pulse in a fibre channel or a change of the electrical voltage on a copper wire) passes through the medium, relative to the speed of light. For optical signals, refractive index is a similar quantity.
Twisted pair copper cabling are known to transmit signals at speeds anywhere between 40% to 70% of that of light. So clearly, there are a lot of variables that come into play here that vary with material used, methods of cabling etc. See this table for reference.
As for your question, a quick wikipedia lookup for fiber optic cables reveals this..
Which at first glance, might seem like faster but does not necessarily mean "always faster" than any/all types of copper cables.
The medium does affect the speed of propagation, but I don't have detailed information on the technologies currently in use.
The rule of thumb is about 2/3 of the speed in vacuum for either coax cable or fiber. No idea for twisted pair.
Summary: A good rule of thumb is roughly 2/3 the speed of light in a vacuum for all these transmission media. Optic fiber is slower than some and faster than others.
Electrical energy normally doesn't flow inside of metals. Poynting-flow diagrams show where the energy flows, and the path(s) traveled by the information carried by that energy, although they are a bit difficult to draw.
As conqenator pointed out,
which gives a wave propagation speed of 1/1.48 and 1/1.46 of the speed of light in a vacuum (0.67 c and 0.68 c) in these regions of a typical optical fiber.
Various popular cables have a wave propagation speed that ranges from 42% to 95% of the speed of light. In particular, 100 Ohm Cat5e cable has a typical propagation speed of 0.64 c. The 300 Ohm Twin-lead has a typical propagation speed of 0.82 c.
dmckee reminded us that it's usually adequate to approximate all of these as around 2/3 c.
So if you use Cat5e cable, bits will arrive slightly later than bits sent through fiber optic. If you use 300 Ohm Twin-lead, bits will arrive slightly before bits sent through fiber optic.
Depends on coaxial cable's dielectric RG58 using PVC will have a Velocity of Propagation Factor(VOPF) of .66 Andrew's FSJ1 having foam dielectric has a VOPF of .78 Fiber Optic has a VOPF of .68. A pulse sent down 100' of RG58 will have 154,045pS delay, FSJ1 will have a 130,346pS delay, Fiber will have a 149,515pS delay