Almarg, an excellent post.
You are correct in interpretation of my 2005 statement, it is precisely what I said AND MEANT at that time.
HOWEVER, my statement then is correct ONLY with respect to lines which have an impedance which matches the load. At the time I made the statement, I had not adequately considered what the extreme mismatch between load, line, and source would do with respect to the settling time of the speaker wire. As it turns out, the only time the naked propagation delay is valid, is when the load matches the line impedance.
My concern is really only for midrange signals. It turns out that settling times for 10 foot zip cords which are terminated in 4 or 8 ohms midband, will be in excess of 5 uSec (Cyril Bateman actually measured this using a reflection bridge) and calculations bring that out in excess of 20 to 50 uSec. Given that humans demonstrate interaural discernment at the 2 uSec level give or take, this settling time falls within the possibility of audibility.
You skin question...I don't see any way to post graphs here, so I'll have to use text.
For a 1.5mm diameter wire at 20 Khz, the exponential solution states that at the center of the wire, there will be a current density which is 20% of the density at the surface.
Using the exact solution, the current density at the center of the wire will be 72% of the surface current density.
The exponential approximation is in error by a factor of 3.6 for a 1.5 mm dia wire at 20Khz.
I am not a cable manufacturer. While I have designed cables, they are always for my own use. I have in the past, provided to at least one (maybe two) cable manufactureres, the equations and understandings to allow them to create any cable of any impedance they wish, either for their own use or for their product line. All information was given freely with no restrictions. Under no circumstances have I profited either monetarily or via materials as payment for information. All materials I have ever used to construct cables, either for test or private use, were funded by myself.
In addition, the information given to that (or those) cable manufacturers is exactly what I have posted on multiple forums for all to use.
The most important thing any technical person can do is to continue learning. Should that learning provide new insights and understandings which conflict with prior knowledge, so be it. Nature of the beast. I am not immune to learning either.
jn
You are correct in interpretation of my 2005 statement, it is precisely what I said AND MEANT at that time.
HOWEVER, my statement then is correct ONLY with respect to lines which have an impedance which matches the load. At the time I made the statement, I had not adequately considered what the extreme mismatch between load, line, and source would do with respect to the settling time of the speaker wire. As it turns out, the only time the naked propagation delay is valid, is when the load matches the line impedance.
My concern is really only for midrange signals. It turns out that settling times for 10 foot zip cords which are terminated in 4 or 8 ohms midband, will be in excess of 5 uSec (Cyril Bateman actually measured this using a reflection bridge) and calculations bring that out in excess of 20 to 50 uSec. Given that humans demonstrate interaural discernment at the 2 uSec level give or take, this settling time falls within the possibility of audibility.
You skin question...I don't see any way to post graphs here, so I'll have to use text.
For a 1.5mm diameter wire at 20 Khz, the exponential solution states that at the center of the wire, there will be a current density which is 20% of the density at the surface.
Using the exact solution, the current density at the center of the wire will be 72% of the surface current density.
The exponential approximation is in error by a factor of 3.6 for a 1.5 mm dia wire at 20Khz.
I am not a cable manufacturer. While I have designed cables, they are always for my own use. I have in the past, provided to at least one (maybe two) cable manufactureres, the equations and understandings to allow them to create any cable of any impedance they wish, either for their own use or for their product line. All information was given freely with no restrictions. Under no circumstances have I profited either monetarily or via materials as payment for information. All materials I have ever used to construct cables, either for test or private use, were funded by myself.
In addition, the information given to that (or those) cable manufacturers is exactly what I have posted on multiple forums for all to use.
The most important thing any technical person can do is to continue learning. Should that learning provide new insights and understandings which conflict with prior knowledge, so be it. Nature of the beast. I am not immune to learning either.
jn