"Robert Morein" wrote in
message news

wrote in message

ups.com...
Robbert "bad scientist" Morein opined:

I speculate this is due to both low capacitance, and
reduced skin
effect.

Mr. Morein: There is no audible skin effect in the
frequency ranges
that audio cables operate in.

I'm sorry, but your assertion is not well grounded.

Two aspects of the above statement are subject to dispute:
1. There is no trivial mathematical basis for it.
2. It may still be true, but there are no publications
that support it. The
publications of Malcolm Hawksford go against the above
statement.

If the poster wishes to claim point "1", the below serves
as a refutation:

The skin depth is defined as the depth at which the
conductivty is reduced
to 1/e from the surface value. e ~ 2.718

The formula varies depending upon the material. Assuming
copper, the skin
depth sigma is given by sigma = 2.6*K1/sqrt(f).
At 10 kHz, the skin depth is .026 inches = .664
millimeters.

HOWEVER, the factor of note, 1/e, is an artifact of the
equation that
determines skin depth. For audibility, it is more relevant
to consider the
attentuation in dB, if the attenuated cross section were
driving an ohmic
load.

The magnitude of the derivative (which is negative) of the
conductivity
curve, is greatest at the boundary. The loss in
conductivity of one factor
of 1.3, is approximately equal to 0.664mm/4 = .166mm at 10
kHz.

For a more lucid treatment, please see:
http://www.st-andrews.ac.uk/~www_pa/...ect/page2.html

"Arny Krueger" wrote in message
...

"Robert Morein" wrote in
message news

wrote in message

ups.com...
Robbert "bad scientist" Morein opined:

I speculate this is due to both low capacitance, and
reduced skin
effect.

Mr. Morein: There is no audible skin effect in the
frequency ranges
that audio cables operate in.

I'm sorry, but your assertion is not well grounded.

Two aspects of the above statement are subject to dispute:
1. There is no trivial mathematical basis for it.
2. It may still be true, but there are no publications
that support it. The
publications of Malcolm Hawksford go against the above
statement.

If the poster wishes to claim point "1", the below serves
as a refutation:

The skin depth is defined as the depth at which the
conductivty is reduced
to 1/e from the surface value. e ~ 2.718

The formula varies depending upon the material. Assuming
copper, the skin
depth sigma is given by sigma = 2.6*K1/sqrt(f).
At 10 kHz, the skin depth is .026 inches = .664
millimeters.

HOWEVER, the factor of note, 1/e, is an artifact of the
equation that
determines skin depth. For audibility, it is more relevant
to consider the
attentuation in dB, if the attenuated cross section were
driving an ohmic
load.

The magnitude of the derivative (which is negative) of the
conductivity
curve, is greatest at the boundary. The loss in
conductivity of one factor
of 1.3, is approximately equal to 0.664mm/4 = .166mm at 10
kHz.

For a more lucid treatment, please see:

http://www.st-andrews.ac.uk/~www_pa/...ect/page2.html

And Dr. Malcolm Hawksford takes the opposite point of view.

"Robert Morein" wrote in
message ...

"Arny Krueger" wrote in message
...

"Robert Morein" wrote
in
message news

wrote in message


ups.com...
Robbert "bad scientist" Morein opined:

I speculate this is due to both low capacitance, and
reduced skin
effect.

Mr. Morein: There is no audible skin effect in the
frequency ranges
that audio cables operate in.

I'm sorry, but your assertion is not well grounded.

Two aspects of the above statement are subject to
dispute:
1. There is no trivial mathematical basis for it.
2. It may still be true, but there are no publications
that support it. The
publications of Malcolm Hawksford go against the above
statement.

If the poster wishes to claim point "1", the below
serves
as a refutation:

The skin depth is defined as the depth at which the
conductivty is reduced
to 1/e from the surface value. e ~ 2.718

The formula varies depending upon the material.
Assuming
copper, the skin
depth sigma is given by sigma = 2.6*K1/sqrt(f).
At 10 kHz, the skin depth is .026 inches = .664
millimeters.

HOWEVER, the factor of note, 1/e, is an artifact of
the
equation that
determines skin depth. For audibility, it is more
relevant
to consider the
attentuation in dB, if the attenuated cross section
were
driving an ohmic
load.

The magnitude of the derivative (which is negative) of
the
conductivity
curve, is greatest at the boundary. The loss in
conductivity of one factor
of 1.3, is approximately equal to 0.664mm/4 = .166mm
at 10
kHz.

For a more lucid treatment, please see:


http://www.st-andrews.ac.uk/~www_pa/...ect/page2.html

And Dr. Malcolm Hawksford takes the opposite point of
view.

Here are the corrections to Hawksford's errors:

http://www.audioholics.com/FAQs/silv...diocables2.php

which references:

http://db.audioasylum.com/cgi/m.mpl?...lm+hawks ford
http://db.audioasylum.com/cgi/m.mpl?...ight=hawksford
http://db.audioasylum.com/cgi/m.mpl?...ight=hawksford

and adds:

"The Hawksford analysis, as printed in the Essex Echo,
neglects to include the storage of energy within the
conductor...the 15 nHenry per foot number with copper. This
is a result of the treatment of the wires as conductors
whose voltage and current arise as a consequence of external
fields. This is not the case for current carrying
conductors. In addition, Hawksford neglected to test
various guages of copper wire conductors, instead,
substituted a steel conductor with a mu of approximately
100. Since the internal inductance is proportional to mu,
the actual inductance he did not accout for was 1.5
microhenries per foot per wire, or 3 microhenries for the
pair. On the assumption he used a meter of wire, that is
about 10 microhenries unaccounted for in his simulation, and
hence, the inductive overshoot in his test. Clearly, had he
modelled this inductance, with the loop resistance of his
wire, he would have found that the wire matches the formula
for inductance provided us by Termen in 1947."

"Arny Krueger" wrote in message
...

"Robert Morein" wrote in
message ...

"Arny Krueger" wrote in message
...

"Robert Morein" wrote
in
message news
wrote in message


ups.com...
Robbert "bad scientist" Morein opined:

I speculate this is due to both low capacitance, and
reduced skin
effect.

Mr. Morein: There is no audible skin effect in the
frequency ranges
that audio cables operate in.

I'm sorry, but your assertion is not well grounded.

Two aspects of the above statement are subject to
dispute:
1. There is no trivial mathematical basis for it.
2. It may still be true, but there are no publications
that support it. The
publications of Malcolm Hawksford go against the above
statement.

If the poster wishes to claim point "1", the below
serves
as a refutation:

The skin depth is defined as the depth at which the
conductivty is reduced
to 1/e from the surface value. e ~ 2.718

The formula varies depending upon the material.
Assuming
copper, the skin
depth sigma is given by sigma = 2.6*K1/sqrt(f).
At 10 kHz, the skin depth is .026 inches = .664
millimeters.

HOWEVER, the factor of note, 1/e, is an artifact of
the
equation that
determines skin depth. For audibility, it is more
relevant
to consider the
attentuation in dB, if the attenuated cross section
were
driving an ohmic
load.

The magnitude of the derivative (which is negative) of
the
conductivity
curve, is greatest at the boundary. The loss in
conductivity of one factor
of 1.3, is approximately equal to 0.664mm/4 = .166mm
at 10
kHz.

For a more lucid treatment, please see:


http://www.st-andrews.ac.uk/~www_pa/...ect/page2.html

And Dr. Malcolm Hawksford takes the opposite point of
view.

Here are the corrections to Hawksford's errors:

http://www.audioholics.com/FAQs/silv...diocables2.php

The corrections are doubtful.

Robert "bad scientist" Morein said: "The corrections are doubtful."




Actually, what's doubtful, is your understanding. You seem to have
many problems in that area, starting with college and on into your
stunted adulthood. Below is a tidbit I found on another group.


Originally posted by Dangerdave on rec.audio.tubes:

For very high frequencies, those where the AC impedance of a wire
becomes significantly higher than DC wire resistance due to skin
effect, the resulting "high frequency wire resistance" is given by
Terman's method:


R = 83.2 * (root (f)) x 10-9
______________
d


This form of the equation applies to cylindrical copper wire.


Where;


R = ohms/centimeter
d = wire diameter in mils
f= Hertz


When "high frequency wire resistance" rises to a value equivalent to
circuit input impedance, the response of the circuit will fall by -3dB
due to wire skin effect.


Therefore, it is useful to know at what frequencies wire skin effect
becomes important when employing hook-up wire in audio frequency
circuits. For some commonly used gauges of hook- up wire, I present
the frequencies where wire skin effect becomes important (-3dB point)
using Terman's method.


For 10cm lengths of copper wire the -3dB frequency is given by:


f=((Rin*d) / (10 * 83.2 * 10E-9)) quantity squared


Table 1
18 Gauge Copper Wire (40.3 mils diameter, 10cm length)


Circuit Input Impedance -3dB point due to wire skin effect
10 Ohm 234,619,140,625,000 Hz
1k Ohm 2,344,619,140,622,500,000 Hz


Table 2
22 Gauge Copper Wire (25.4 mils diameter, 10cm length)


Circuit Input Impedance -3dB point due to wire skin effect
10 Ohm 93,201,044,748,200 Hz


1k Ohm 932,010,447,482,000,000 Hz


Table 3
26 Gauge Copper Wire (16 mils diameter, 10cm length)


Circuit Input Impedance -3dB point due to wire skin effect
10 Ohm 36,982,248,520,800 Hz
1k Ohm 369,822,485,208,000,000 Hz


Table 4 0.13cm dia wire silver wire (5.1mils dia., 10cm length)


Circuit Impedance -3dB point due to wire skin effect
1k Ohm 3,757,4542,344,700,000 Hz


By simple inspection of results it is clear that skin effect plays no
role in audio frequency circuits interconnected with 10cm lengths of
hook-up wire. The frequencies involved, TRILLIONS of Hertz or more,
do not exist in audio circuits (except as noise). To put things in
perspective, the highest frequency humans can hear is 20 THOUSAND
Hertz.


For circuits of higher input impedance, skin effect becomes even less
important.


Interestingly, application of Terman's method demonstrates that tiny
gauge wire (Table 4) is about 100x worse for skin effect, as compared
to normal gauge hook-up wire. The reason is simple. Bigger wires
have a larger circumference. Skin effect crowds current to the edges
of the conductor. By Terman's method, when the circumference is
larger, there is more material conducting current. If you want to
reduce the impedance of hook-up wire in your audio frequency circuits,
choose a larger diameter.


Using silver makes no difference. With silver or copper, skin effect
play no role in audio frequency circuits interconnected with hook-up
wire.


An RF rule of thumb is that skin effect becomes important when the
wavelength approaches the diameter of the wire. I think it is a good
rule of thumb, however, some have taken issue because it may produce
results that are "many orders of magnitude" in error. Correction
noted. By application of Terman's method it is clear that the minimum
frequency for skin effect in audio circuits is not BILLIONS of Hertz,
it is, more precisely TRILLIONS of Hertz, or more.


Inductance, capacitance and resistance of hook-up wire is millions of
times more important than skin effect to the sound and electrical
response of audio circuits. To improve your audio circuit, use normal
gauge hook-up wire, and pay attention to routing and placement.


References:
Frederick Emmons Terman, Sc.D.
Professor Of Electrical Engineering
Executive Head, Electrical Engineering Department, Stanford University
Director, Radio Research Laboratory, Harvard University
President, Institute of Radio Engineers
Terman, Radio Engineers' Handbook, McGraw-Hill

In short Mr. Morein, you are wrong again. Skin effect is a problem at
radio frequencies, not audio frequencies.