tomp wrote:
As David mentioned, the characteristic impedance has nothing to do with distance. The cable looks like an infinite number of series inductances paralleled by an infinite number of capacitances. No many how many you cut off the combination of each inductor and capacitor still yields the same impedance. What does change with length is attenuation of the signal.
I was referring to transmission lines. We can discuss transmission lines when the cable is a length that is significant in terms of wavelength, such that the wave nature of the AC signal becomes apparent. Voltage and current, hence impedance will vary at different distances along the line. The length of the line becomes significant for impedance matching considerations.
There is more going on than varying attenuation with changes in length, in other words,
A half wave transmission line is a step up transformer, so a 50 ohm nominal load is transformed to 3000 or so ohms at the end of the half wave section.
Now an
electrical wavelength at 20hz, assuming that the propagation through the wire is at the speed of light is 186,000 mi/20 or 9300 miles.
Multiply by maybe 0.8 to account for the
velocity factor of the wire and make it 7440 miles of speaker wire.
That's for one channel, of course.
If you cut that wire the impedance will no longer be 8 ohms @20hz at the amplifier end. In fact, it will only be 8 ohms with the entire wavelength of cable.
And for any other frequency, the wire wil no longer be a full wavelength, so you will have to calculate the complex impedance of the speaker at each frequency and then look at the impedance transformation characteristics of the line....unless we only want to listen to 20hz tones.
To counter resistive losses, better make sure that the wire is #0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 gauge OFC, although 5N silver would be preferable in terms of detail and silvery highs.
Also, don't forget, it is usually a good idea to bi-wire!
The question of characteristic impedance is a somewhat separate issue,. I suppose you could look for reflection with a pulse reflectometer and find a configuration that will minimize reflections at 8 ohms. Too bad most speakers will only be 8 ohms at one point, if that, otherwise there will be reflections. And you will need a few thousand miles of it to make a
transmission line for AF.
Speakers won't have a resistive impedance, except for David's weird Polks, so you will have to take the ratio of capacitive to inductive reactances into account. But since that will vary with frequency, things become very tricky indeed.
The transmission line concept doesn't seem to have any relevance for audio frequency, thank god! I'm not sure that controlled impedance cable do either, but it may seem a good marketing ploy to some. If one could sell a 15000 thousand miles of high end cable at a time, we're talking some serious bank!