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?

Basically the maximum range comes down to a few factors:
• Minimum power required by the headphone speakers for acceptable sound.
• Maximum power output by the MP3 player.
• Power consumption of the cable (watts/metre).

Chances are you'd get some of these figures by deriving them from operating voltages and max current outputs etc.

If you have these things then you can shift them around to get:
(Maximum Output) = (Minimum Input) + (Cable Power Consumption per Metre)*(Maximum Cable Length)
Which rearranges to:
(Maximum Cable Length) = ((Maximum Output) - (Minimum Input))/(Cable Power Consumption per Metre)

>>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.

Can anyway give me some numbers?
Like a minimum and a maximum.

>>3
I'm an engineer, not a theoretical scientist.
I think considering the potential temperature shift for a low power app like this we can probably treat the cabling as perfect, not like the silly non-ohmic conductor it really is. I don't even want to think about other effects like signal frequency component distribution across the cable diameter.

>>4
For a small MP3 player I don't think I'd want to use anything longer than about 5 metres, although if you're using good quality gear it might be able to hack a bit more. The longest I've tried successfully was about 8-10m, but that was fed into a stereo anyway, so the signal could be reamped.

>>5
5 meters? You're kidding. That little?

Portable MP3 players are designed to be used in close proximity to the speakers - that's kinda the point. As such they don't typically have a high output capacity.
5 metres is what's usually recommended for a USB cable powered directly from a PC, although a good MP3 player will no doubt be able to handle at least a slightly higher current.

I once used a Discman and an old set of headphones to connect the output of the Discman up to the speakers of a broken stereo cabinet. When the Discman was hooked up using the supplied power adapter, the music could get really loud, but when using headphones, it didn't sound any louder than normal.

OP, the only way to get hard numbers, without doing some serious number crunching, is to actually try it. Use a set of old headphones, splice the cable with a long length of wire bought from a dollar store.