Audio signal range

Say you plug headphones with infinitely extendable cable length to a regular MP3 player, how far will the signal travel from the player through the cable until it ceases to be heard?

>>2
You're missing a few terms.  The first thing that comes to mind is the temperature-resistance variance of the cable.

Your so-called maximum point will actually varying with time, and will perhaps even oscillate, depending on the terms which affect transmission.