The reason why I ask this is because I recently read that the effective length of a transmission line is the actual length of the line time the sqrt of the core permeability. (Ref "A tutorial on transmission line transformers" -equation 5)

So if a core with a μe of 2500 were used this would reduce the required length of the line by a factor of 50.

Then you could take a 1000 ft cable and it's effective length would be 50,000 feet (9.49 miles). With a velocity factor of .7 this equates to a full wave frequency of 13.7kHz if my math is correct. So a frequency 1/4 of 13.7kHz (3.4kHz) could be used to form a quarter wave line?