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Author Topic: Conductance in different materials.  (Read 6169 times)

ammitsboel

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Conductance in different materials.
« on: January 29, 2005, 06:15:13 AM »

I have a strictly technical question.

What is the conductance in silver, cobber and gold?
And what conducts best?
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ammitsboel

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Re: Conductance in different materials.
« Reply #1 on: January 29, 2005, 11:51:30 AM »

Found this on the net:

Resistivity in ohm-meters
Metals:

           
Aluminum 2.65e-8

           
Beryllium 4.0e2.65e

           
Beryllium-copper

           
Brass 70% copper, 30% zinc

           
Copper 1.673e2.65e-8

           
Gold 2.35e2.65e-8

           
Iron 9.71e-8

           
Lead 20.648e-8

           
Magnesium 4.45e-8

           
Molybdenum 5.34e-8

           
Monel

           
Nickel 6.84e-8

           
Platinum 10.6e-8

           
Silver 1.59e-8

           
Stainless Steel-321

           
Stainless Steel-410

           
Steel, low carbon

           
Tin 11.0e-8

           
Titanium 42.0e-8

           
Tungsten 5.40e-8

           
Zinc 5.964e-8


So i guess i found what I was looking for.
Please post any comments you might have.

Best Regards
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Brian Roth

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Re: Conductance in different materials.
« Reply #2 on: January 30, 2005, 03:17:05 AM »

Interesting, but why the question?  It becomes an issue when transmitting power from the utility company's "generator station" to your home, but is otherwise moot with audio (excepting loudspeaker wiring).

Bri

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ammitsboel

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Re: Conductance in different materials.
« Reply #3 on: January 30, 2005, 05:44:59 AM »

My question was just out of curiosity.
And i had a discussion where one was claiming that copper was a better conductor than silver.
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Sahib

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Re: Conductance in different materials.
« Reply #4 on: January 30, 2005, 07:36:16 AM »


Silver is the best conductor as it has the least resistance.

Top three conductors and their relative conductances are;

1.Silver 100%
2.Copper 98%
3.Gold 78%

Cemal
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Mike Mermagen

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Re: Conductance in different materials.
« Reply #5 on: January 30, 2005, 09:13:32 PM »

Brian Roth wrote on Sun, 30 January 2005 08:17

Interesting, but why the question?  It becomes an issue when transmitting power from the utility company's "generator station" to your home, but is otherwise moot with audio (excepting loudspeaker wiring).

Bri



Brian,
Since an entire audio chain is based on electrical signals over some kind of metal conductor, I'm not sure why you would say the point is "moot" for audio and not for loudspeaker wiring.

Mike
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David Satz

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Re: Conductance in different materials.
« Reply #6 on: January 30, 2005, 10:49:03 PM »

Mike, [a] hi again, and it's because when you're feeding a signal to a relatively high-impedance load such as the input of a power amplifier, a few Ohms of resistance in the line won't affect the signal enough to matter. You can't hear a loss of, say, 0.001 dB even if it's frequency-dependent.

However, loudspeakers aren't a high-impedance load, so the impedance of speaker cable can become an appreciable fraction of their impedance--at which point the losses in the cable can become audible, or at least worthy of a thought.

It's basically Ohm's Law in action. If you've studied any electronics I don't want to start spelling that all out, but if you haven't, then we can certainly talk it through. At any rate it's an area of audio in which theory and practice (i.e. audible results) get along just fine.

--best regards
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Brian Roth

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Re: Conductance in different materials.
« Reply #7 on: January 31, 2005, 02:52:16 AM »

Thanks, David, for voicing my exact thoughts.  I am VERY suspicious of claims made that a few/dozen feet of cable running analog line level signals can cause an appreciable degradation of the signal...unless it was built with "baling wire"  (or, in the Southwest where we have large ranches: "bob war"  AKA barbed wire  <g>).

I will allow that perhaps the insulation can have an effect due to capacitance loading, but that then puts the onus back at the device driving the cable.

But, I think there is some sort of Placebo Effect once someone pays $10/foot for fancy Oxygen-Free gold-plated wire with cross-twisted teflon insulation that has been pissed upon by vestal virgins under the new moon before being cryogenically (sp?) treated.  "By Gawd, I paid a FORTUNE for this cable, so it sounds GREAT!"

Bri





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ammitsboel

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Re: Conductance in different materials.
« Reply #8 on: January 31, 2005, 04:31:46 AM »

Since this is a strictly technical forum the question was just strictly technical.
I don't think that the audible differences when comparing copper to silver is related to the conductance.
Maybe it can be measured by other parameters?

Best Regards
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Joe Crawford

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Re: Conductance in different materials.
« Reply #9 on: January 31, 2005, 01:12:32 PM »

Actually, when you’re talking about cable used to transfer audio around the studio, there are four characteristics involved: resistance, capacitance, susceptibility to noise, and the fourth I think is (or at least used to be) called skin effect.  I think we all pretty well understand the effects of the first three.

If Dan is around maybe he can help me with the fourth one.  I’m a bit rusty on the skin effect.  I know that direct current is evenly distributed throughout the cross section of a conductor.  But, alternating current is different.  As the frequency of AC increases, the current tends to travel more in and along the surface of a conductor.  I know the skin effect has to be considered at radio frequencies, but does it also have a noticeable effect at audio frequencies?  Can we generally ignore it, or is it already covered by using the impedance of the cable?

Joe Crawford

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David Satz

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Re: Conductance in different materials.
« Reply #10 on: January 31, 2005, 01:49:17 PM »

Joe, it can easily be shown that skin effect is several orders of magnitude below significance at all audio frequencies--even the highest audio frequencies that dogs and bats can hear--for all possible terrestrial cable lengths. For transmission lines carrying VHF and higher it's a different story. But with baseband analog audio it's not worth worrying about unless your cable is long enough to reach between planets--and then you might have some other problems to deal with, such as how to unkink it after a meteor shower.

Even baseband video frequencies aren't affected significantly unless transcontinental cables are your thing--and there again, I think that you might be more worried about sharks munching on your cable than high-frequency losses due to skin effect.

As a result I find that skin effect provides a good quick litmus test for rudimentary truth in advertising: If a cable manufacturer waves that particular bugaboo in front of you when talking about baseband analog audio cables, you can cross them off your list in a hurry.

--best regards
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Sahib

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Re: Conductance in different materials.
« Reply #11 on: January 31, 2005, 02:19:37 PM »

Joe Crawford wrote on Mon, 31 January 2005 18:12

Actually, when you’re talking about cable used to transfer audio around the studio, there are four characteristics involved: resistance, capacitance, susceptibility to noise, and the fourth I think is (or at least used to be) called skin effect.  I think we all pretty well understand the effects of the first three.

If Dan is around maybe he can help me with the fourth one.  I’m a bit rusty on the skin effect.  I know that direct current is evenly distributed throughout the cross section of a conductor.  But, alternating current is different.  As the frequency of AC increases, the current tends to travel more in and along the surface of a conductor.  I know the skin effect has to be considered at radio frequencies, but does it also have a noticeable effect at audio frequencies?  Can we generally ignore it, or is it already covered by using the impedance of the cable?

Joe Crawford




Skin effect is the tendency of the alternating current to flow near or on the surface of the conductor at high frequencies. At 1Khz the current flows through the outside skin to a depth of 0.9mm. At 1Mhz the skin depth is 0.07mm. So it seems like it does not have a hugely concerning effect on audio frequency provided that the thickness of the conductor is sufficient to serve it.

Information is taken from my electronic tables and formulas.
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Joe Crawford

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Re: Conductance in different materials.
« Reply #12 on: February 01, 2005, 12:14:03 PM »

Thanks David & Sahib.  That pretty well covers the skin effect.  And, it looks like Dan has covered impedance & termination in the ‘Word Clock, Super Click & Termination’ thread.

I feel much safer now in buying a few dozen more Munster cables.  Now if I can just figure out how to fit those #4 gage, gold twinaxes in my patch panels.  Wait, maybe it'll work better for mic cable if you don’t mind that welding shop look.  At least it'll be foot-proof.

Anyway, thanks again guys...

Joe Crawford
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danlavry

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Re: Conductance in different materials.
« Reply #13 on: February 02, 2005, 02:24:24 PM »

The figures for skin depth you mentioned are for a specific wire gauge. The “mechanics” of skin effect is as follows:

There is an electrostatic force between electrons, and that force is making them “move away from each other”. You put a bunch of electrons in a conductor (such as a wire), and they want to keep separate from each other, while remaining inside the conductor, so they still will “even out” in terms of the spacing between them.

When you run DC down a wire, the same holds true. The cross section of the wire is “evenly distributed” in terms of electron spacing, so the whole copper gets used to conduct current.

But when you run AC, the electrons start moving back and forth, and the acceleration (and deceleration) of each electron produces a new force. This force is magnetic. The faster the acceleration (deceleration) the stronger the force. The combined force due to all the electrons makes the repulsion force at the center of the conductor be the strongest, and it gets weaker as you get away from center.

If it were only up to the magnetic force, all the electrons would end up right at the conductor surface. But the other force, the electrostatic one, does not let them be so near each other. The result is a balance between electrostatic and electromagnetic behavior. The electrostatic is a fixed force, the electromagnetic varies with frequency. The dependency on frequency is not linear – the skin effect goes up with the square root of the frequency (often expressed in MHz).

The dimensions of the wire (such as wire gauge, which relates to cross sectional area) do count. One way to relate to skin effect is as a multiplier of the DC resistance. The AC resistance will be the DC resistance multiplied by the square root of the frequency and also multiplied by a K factor. The K constant is different value for different wire gauges.

Say you have an 100 feet of an 18 gauge wire. The DC resistance is about 0.65 Ohms. The K factor for 18AWG wire is about 11. So the AC resistance is:
At DC .65 Ohms, at 20KHz it will become 1 Ohm, at 100KHz, 2.25 Ohm, at 1MHz we have 7 Ohms, 22 Ohms at 10MHz…

So yes, you may not want to use 100 feet of 18AWG for the speakers, but 10 feet is (0.1Ohm) probably fine, from skin effect standpoint. A 10AWG at 10feet yields DC resistance of 1 milliohm and with skin effect it comes to 4 milliohms, so even 100 feet of 10AWG is only 40 milliohms at 20 KHz (it is really 50 feet each direction).

Skin effect is “non capacitive” and “non inductive”. It is resistive only. No phase issues what so ever.

I guess one way to look at skin effect is through the “glasses of” “skin depth”. Skin depth is a bit of a simplification, an “average” because the wire is not really divided into 2 distinct zones (“electron flow zone” and “no electron zone”). A few electrons do run near the center, and the distribution is more gradual then a brick wall. But skin depth is a reasonable way to view skin effect.

Having said all of that, skin efect really does not matter for audio signals!

Regards
Dan Lavry
 

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Sahib

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Re: Conductance in different materials.
« Reply #14 on: February 03, 2005, 06:33:28 AM »

danlavry wrote on Wed, 02 February 2005 19:24



Say you have an 100 feet of an 18 gauge wire. The DC resistance is about 0.65 Ohms. The K factor for 18AWG wire is about 11. So the AC resistance is:
At DC .65 Ohms, at 20KHz it will become 1 Ohm, at 100KHz, 2.25 Ohm, at 1MHz we have 7 Ohms, 22 Ohms at 10MHz…

So yes, you may not want to use 100 feet of 18AWG for the speakers, but 10 feet is (0.1Ohm) probably fine, from skin effect standpoint. A 10AWG at 10feet yields DC resistance of 1 milliohm and with skin effect it comes to 4 milliohms, so even 100 feet of 10AWG is only 40 milliohms at 20 KHz (it is really 50 feet each direction).
 



Dan,

Many thanks for this. Yes the formula book I have has limited info on this issue. Can you recommend me a better one? What do you use?

Regards,
Cemal
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danlavry

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Re: Conductance in different materials.
« Reply #15 on: February 03, 2005, 08:38:51 PM »

Sahib wrote on Thu, 03 February 2005 11:33

danlavry wrote on Wed, 02 February 2005 19:24



Say you have an 100 feet of an 18 gauge wire. The DC resistance is about 0.65 Ohms. The K factor for 18AWG wire is about 11. So the AC resistance is:
At DC .65 Ohms, at 20KHz it will become 1 Ohm, at 100KHz, 2.25 Ohm, at 1MHz we have 7 Ohms, 22 Ohms at 10MHz…

So yes, you may not want to use 100 feet of 18AWG for the speakers, but 10 feet is (0.1Ohm) probably fine, from skin effect standpoint. A 10AWG at 10feet yields DC resistance of 1 milliohm and with skin effect it comes to 4 milliohms, so even 100 feet of 10AWG is only 40 milliohms at 20 KHz (it is really 50 feet each direction).
 



Dan,

Many thanks for this. Yes the formula book I have has limited info on this issue. Can you recommend me a better one? What do you use?

Regards,
Cemal




The reference I use for skin effect is mostly “Reference Data For Radio Engineers”, a classic reference by Howard W. Sams Inc publications, which is a subsidiary of ITT.
It gives one the tools to figure skin effect at any diameter and for any standard material.
It is more complicated then a single formula, with correction factors for other considerations.

One such consideration is the case of parallel wires. Clearly, if the parallel wires are far away from each other, the interactive forces between electrons in one wire have near zero impact on electrons in the other wire. As a rule, a distance of 10 times the diameter between wires is considered far enough for any interaction. But at a distance of say about 4 times the diameter, the cross influence between conductors carrying current in the same direction is starting to be noticed, and that is an important factor for stranded high frequency wires manufacturers... A lot of thin wires do yield more surface area then one thick solid wire with the same overall diameter, yet the thickness and distance between can be optimized for high frequency. Even a simple wire design can be such a complicated thing… BUT NOT FOR AUDIO FREQUENCIES…  

There are of course many other references with more direct results – already computed For standard copper wire of standard AWG diameters.

As I mentioned, the concept of skin depth is not a “brick wall” divding the copper into conduction and non conduction zones. The current density decreases as we get nearer the wire center, and the skin depth is where the current density is at 37% compared to the value at the surface (37% is 1/e). Now that skin depth concept is based on the assumption that the wire diameter is significantly larger then the skin depth. Skin depth could be misleading to the novice. Skin depth of say 1mm does not mean you can get by with a 1mm or 2mm wire diameter. You need at least 3mm, and 4-5mm diameter is better. Going any further may be a waste of material…

The important concept is RAC/RDC – the ratio between DC resistance and AC resistance at a given frequency. BUT NOT FOR AUDIO FREQUENCIES (where skin effect is negligable)…

The reason people talk about skin effect in audio is a MARKETING one, nothing else!

Regards
Dan Lavry
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David Satz

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Re: Conductance in different materials.
« Reply #16 on: February 10, 2005, 09:52:00 AM »

Dan,

It was great to see/hear you at the New York AES meeting earlier this week. Thank you for coming in and speaking with us.

--Regarding skin effect, the reference numbers for the K factor that you gave three messages back were for a single, solid conductor, no? In stranded wire, skin effect is lessened even further because it really applies to each strand individually. So the use of stranded wire not only helps to prevent breakage when a wire is bent, but it also brings the wire's resistance at high frequencies considerably closer to its DC resistance.

Stranded wire is what nearly everybody uses for audio cables. So if those K numbers were for solid conductors, then in practice, skin effect at audio frequencies matters even less than they would indicate. Maybe that 100-foot "zip cord" speaker wire isn't so bad after all!

--best regards
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danlavry

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Re: Conductance in different materials.
« Reply #17 on: February 11, 2005, 06:30:24 PM »

David Satz wrote on Thu, 10 February 2005 14:52

Dan,

It was great to see/hear you at the New York AES meeting earlier this week. Thank you for coming in and speaking with us.

--Regarding skin effect, the reference numbers for the K factor that you gave three messages back were for a single, solid conductor, no? In stranded wire, skin effect is lessened even further because it really applies to each strand individually. So the use of stranded wire not only helps to prevent breakage when a wire is bent, but it also brings the wire's resistance at high frequencies considerably closer to its DC resistance.

Stranded wire is what nearly everybody uses for audio cables. So if those K numbers were for solid conductors, then in practice, skin effect at audio frequencies matters even less than they would indicate. Maybe that 100-foot "zip cord" speaker wire isn't so bad after all!

--best regards


quote title=David Satz wrote on Thu, 10 February 2005 14:52]Dan,

It was great to see/hear you at the New York AES meeting earlier this week. Thank you for coming in and speaking with us.

--Regarding skin effect, the reference numbers for the K factor that you gave three messages back were for a single, solid conductor, no? In stranded wire, skin effect is lessened even further because it really applies to each strand individually. So the use of stranded wire not only helps to prevent breakage when a wire is bent, but it also brings the wire's resistance at high frequencies considerably closer to its DC resistance.

Stranded wire is what nearly everybody uses for audio cables. So if those K numbers were for solid conductors, then in practice, skin effect at audio frequencies matters even less than they would indicate. Maybe that 100-foot "zip cord" speaker wire isn't so bad after all!

--best regards[/quote]


Hello David,

It was great to be in NY, and I lucked out missing the cold weather.

Yes I was talking about a single solid wire, and the concept of "skin depth" is also for a single wire.
There are at least 2 reasons for the use of stranded wires instead of solid:

The first one is most obvious - mechanical flexibility (such as for the AC chords we use at home to light the lamps, power the TV......) the 60Hz AC application has nothing to do with skin effect.

The second reason is for carrying high frequency signals, way faster then audio.

If we take a circular cross sectional area of a given diameter, and fill it with solid copper, the circumference is well known, and so is the surface of that wire. It is also correct to say that one may fill the same cross sectional area with a tight fit of many smaller diameter wires and the combined surface will be much higher which will reduce the skin effect.

However, it is a common misconception that the skin effect improvement is proportional to the combined surface area packed into the available space. There are 2 reasons why the relationship is not linear:
1. Each wire strand must have enough diameters to take advantage of the "skin depth" concept and in practical terms, each strand must be at least 3-4 times the skin depth, or else the electrons will not "be concentrated on the skin".
2. The resistance of say 10 wire strands is not always one tenth of a single strand because when you "bunch wires together" the electrons on one wire interact with electrons from other wire strands with forces that counteract the multi wire improvement.

So yes, stranded wire has lower skin effect, but a wire design can be optimized electrically for say 10MHz, for 100Mhz, for 1GHz all calling for different dimensions, and there is of course a whole other set of requirements namely mechanical considerations...

Having said all that, skin effect is of no consequence for audio frequencies. It is a marketing hype!

Regards
Dan Lavry
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ammitsboel

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Re: Conductance in different materials.
« Reply #18 on: February 11, 2005, 08:17:19 PM »

Is there a scientific explanation to the sound differences in stranded and solid core cables? let's just say speakers cables.
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bblackwood

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Re: Conductance in different materials.
« Reply #19 on: February 12, 2005, 08:04:31 AM »

ammitsboel wrote on Fri, 11 February 2005 19:17

Is there a scientific explanation to the sound differences in stranded and solid core cables? let's just say speakers cables.

I think you'd first have to show that there was scientific proof of said difference. To my knowledge, no one has ever passed a true double-blind test on similar (low capacitance) cables...
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danlavry

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Re: Conductance in different materials.
« Reply #20 on: February 12, 2005, 08:31:26 PM »

Summary:

The sonic differences one hears, and the electrical differences one measures regarding speaker wires have more to do with the concept of "wire pair" than an individual wire. The characteristics of a wire pair are defined by their relative geometry. A proper test comparing solid to stranded wire calls for identical geometries. Below is the only explanation I can come up with for sonic differences due to reasonable gauge speaker wire:

Details:

I previously stated that speaker wire performance is not influenced by skin effect. In another thread I talked about capacitance, and at very low impedances, capacitance of the cable (especially with short distances such as speaker cables) is not going to alter the signal by any amount you can hear. That leaves resistance and inductance.

Speakers are complicated devices. A good approximation to view a speaker (a driver), often used by speaker designers is an equivalent circuit developed by Thiele and Small, and the equivalent circuit parameters are often available from the driver manufacturers. Note that the parameters consist of both electrical and electromechanical resistances, inductances and capacitance so that the designer ends up with a electrical network describing a speaker driver. Each driver (be it a sub woofer, woofer or tweeter) is far from optimal or desirable device, having an electrical peak (resonance), a mechanical resonance and certainly a need to be corrected (compensated) with a network. The compensation is mostly done via conjugate filters - a circuit made of "real" resistors, capacitors and sometimes inductors to "counteract" the combination of electric and electromechanical behavior of the driver. One such common network is a Zobel Circuit, but there are others... So a speaker cabinet can be looked at as 2-3 drivers with some crossover networks and compensation networks, and one of the goals is to have a constant restive impedance across the audio range (such as 8 Ohms)...

I looked at some of the networks wondering about how much series resistance and inductance it would take to alter the response or ruin the compensation of the drivers or the crossover networks. At first glance it does not seem possible that the resistance of a 10-30 feet of say 12 gauge wire could do much at all. But I would say it is possible to have just enough inductance to interact with the network in a way that will cause a little bit of high frequency loss. I am including a plot for a very simplistic model, assuming a perfect speaker (8 Ohm resistive load over the audio range) and the effect of a cable inductance, assuming 1uH per foot. The picture shows amplitude response to 20KHz for 10feet, 20 feet and 30 feet distance.

Note that we are talking about PASSIVE speakers. All I am saying is NOT true for active (powered speaker), where the whole issue of cable type goes away completely.

Also Note that while resistive variations due to wire are very small to impact the frequency response, a power amplifier output impedance can have an impact.

Below: the red line (10 feet cable) shows around .1dB loss at 20KHz. The Black (30 feet cable) line shows almost a dB at 20Kh and a 1/4dB at 10KHz. It all assumes 1uH per foot and an ideal 8 Ohms speaker. This plot is just a rough first aproximation.  

index.php/fa/667/0/  

I did not answer your question directly regarding solid vs. stranded wire. However, while this answer is indirect, it may hold a key to sonic differences. I assumed (for the graph) 1uH per foot, which is "in the ball park". A reduction would make the response flatter and more inductance would make it worse.

As a rule, a pair of conductors have less inductance when they are closer. Taking 2 individual conductors such as solid copper with thick insulation, and running the "hot" and the "return" far apart yields more inductance than a tightly paralleled pair.

I wonder if the conclusion regarding solid vs stranded resulted from a test where other variables (such as difference in inductance) were unnoticed.

Best Regards
Dan Lavry
www.lavryengineering.com
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