Yes. It is probably less than 1 cm/second. It is called the electron drift velocity. As in a steel bar, where if you hit one end with a hammer, the sound wave travels up it at the speed of sound in steel and will send an object off the other end very quickly, the whole bar only starts to move much more slowly. The electrons only travel slowly, but push the next electron and the one after that etc. very quickly. I don't think the frequency of the signal affects the drift velocity much, until perhaps the period is less than the mean-free-path time of the electrons, when the electrons might travel even more slowly.
Malcolm White,
Many thanks. But there is or there is not a fundamental formula to make this calculus?
Yes there are lots
See this for a start
https://www.macmillanlearning.com/studentresources/college/physics/tiplermodernphysics6e/classial_concept_review/chapter_10_ccr_10_mean_free_path.pdf
Electrons in metal conductors experience quantum mechanics defined and also chaotic, thermall agitated motion at speed with charteristic value know as Fermi velocity whict is about 1.5 * 104 m/sec for copper. Any practical electrical current will be a tiny average drift on top of it, well below mm/sec (think how slowly electrosis move bulk material). https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Book%3A_Introduction_to_Inorganic_Chemistry_(Wikibook)/06%3A_Metals_and_Alloys-_Structure_Bonding_Electronic_and_Magnetic_Properties/6.06%3A_Conduction_in_Metals
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