Science that explains why we hear differences in cables?


Here are some excerpts from a review of the Silversmith Audio Fidelium speaker cables by Greg Weaver at Enjoy The Music.com. Jeff Smith is their designer. I have not heard these cables, so I don’t have any relevant opinion on their merit. What I find very interesting is the discussion of the scientific model widely used to design cables, and why it may not be adequate to explain what we hear. Yes it’s long, so, to cut to the chase, I pulled out the key paragraph at the top:


“He points out that the waveguide physics model explains very nicely why interconnect, loudspeaker, digital, and power cables do affect sound quality. And further, it can also be used to describe and understand other sonic cable mysteries, like why cables can sound distinctly different after they have been cryogenically treated, or when they are raised off the floor and carpet.”


“One of the first things that stand out in conversation with Jeff about his cables is that he eschews the standard inductance/capacitance/resistance/impedance dance and talks about wave propagation; his designs are based solely upon the physics model of electricity as electromagnetic wave energy instead of electron flow.


While Jeff modestly suggests that he is one of only "a few" cable designers to base his designs upon the physics model of electricity as electromagnetic wave energy instead of the movement, or "flow," of electrons, I can tell you that he is the only one I’ve spoken with in my over four decades exploring audio cables and their design to even mention, let alone champion, this philosophy.


Cable manufacturers tend to focus on what Jeff sees as the more simplified engineering concepts of electron flow, impedance matching, and optimizing inductance and capacitance. By manipulating their physical geometry to control LCR (inductance, capacitance, and resistance) values, they try to achieve what they believe to be the most ideal relationship between those parameters and, therefore, deliver an optimized electron flow. Jeff goes as far as to state that, within the realm of normal cable design, the LRC characteristics of cables will not have any effect on the frequency response.


As this is the very argument that all the cable flat-Earther’s out there use to support their contention that cables can’t possibly affect the sound, it seriously complicates things, almost to the point of impossibility, when trying to explain how and why interconnect, speaker, digital, and power cables have a demonstrably audible effect on a systems resultant sonic tapestry.


He points out that the waveguide physics model explains very nicely why interconnect, loudspeaker, digital, and power cables do affect sound quality. And further, it can also be used to describe and understand other sonic cable mysteries, like why cables can sound distinctly different after they have been cryogenically treated, or when they are raised off the floor and carpet.


As such, his design goal is to control the interaction between the electromagnetic wave and the conductor, effectively minimizing the phase errors caused by that interaction. Jeff states that physics says that the larger the conductor, the greater the phase error, and that error increases as both the number of conductors increase (assuming the same conductor size), and as the radial speed of the electromagnetic wave within the conductor decreases. Following this theory, the optimum cable would have the smallest or thinnest conductors possible, as a single, solid core conductor per polarity, and should be made of metal with the fastest waveform transmission speed possible.


Jeff stresses that it is not important to understand the math so much as it is to understand the concept of electrical energy flow that the math describes. The energy flow in cables is not electrons through the wire, regardless of the more common analogy of water coursing through a pipe. Instead, the energy is transmitted in the dielectric material (air, Teflon, etc.) between the positive and negative conductors as electromagnetic energy, with the wires acting as waveguides. The math shows that it is the dielectric material that determines the speed of that transmission, so the better the dielectric, the closer the transmission speed is to the speed of light.


Though electromagnetic energy also penetrates into and through the metal conductor material, the radial penetration speed is not a high percentage of the speed of light. Rather, it only ranges from about 3 to 60 meters per second over the frequency range of human hearing. That is exceptionally slow!


Jeff adds, "That secondary energy wave is now an error, or memory, wave. The thicker the conductor, the higher the error, as it takes longer for the energy to penetrate. We interpret (hear) the contribution of this error wave (now combined with the original signal) as more bloated and boomy bass, bright and harsh treble, with the loss of dynamics, poor imaging and soundstage, and a lack of transparency and detail.


Perhaps a useful analogy is a listening room with hard, reflective walls, ceilings, and floors and no acoustic treatment. While we hear the primary sound directly from the speakers, we also hear the reflected sound that bounces off all the hard room surfaces before it arrives at our ears. That second soundwave confuses our brains and degrades the overall sound quality, yielding harsh treble and boomy bass, especially if you’re near a wall.


That secondary or error signal produced by the cable (basically) has the same effect. Any thick metal in the chain, including transformers, most binding posts, RCA / XLR connectors, sockets, wire wound inductors, etc., will magnify these errors. However, as a conductor gets smaller, the penetration time decreases, as does the degree of phase error. The logic behind a ribbon or foil conductor is that it is so thin that the penetration time is greatly reduced, yet it also maintains a large enough overall gauge to keep resistance low.”


For those interested, here is more info from the Silversmith site, with links to a highly technical explanation of the waveguide model and it’s relevance to audio cables:


https://silversmithaudio.com/cable-theory/


tommylion
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I started to watch the video but the first statement in the video: "The square wave and the sine wave are the same thing only with distortion" is complete lunacy.


OK, i would not state it that way. But...., step back. A distortion is a "change or difference in an electrical signal". Well, its a big difference no doubt, but i think that’s his point. Maybe a stretch, but valid/true. Just sayin’

djones514 already expanded on my concern with equating a square wave to a sine wave in the video.

The square wave and sine wave are not the same thing the square wave simulates all audio frequencies and MORE, the and more is infinite bandwidth. The test shown in that video is not band limited to audio frequencies The refections shown are above 50kHz.

Using a square wave as a test signal produces harmonics with frequency content well beyond audible frequencies, As djones514 already pointed out, the  refections shown in the video are above audible frequencies. maybe your cat and dog may be able to hear the difference, but not you.

from wikipedia:

The ideal square wave contains only components of odd-integer harmonic frequencies (of the form 2π(2k − 1)f). Sawtooth waves and real-world signals contain all integer harmonics.

A curiosity of the convergence of the Fourier series representation of the square wave is the Gibbs phenomenon. Ringing artifacts in non-ideal square waves can be shown to be related to this phenomenon. The Gibbs phenomenon can be prevented by the use of σ-approximation, which uses the Lanczos sigma factors to help the sequence converge more smoothly.

An ideal mathematical square wave changes between the high and the low state instantaneously, and without under- or over-shooting. This is impossible to achieve in physical systems, as it would require infinite bandwidth.

Animation of the additive synthesis of a square wave with an increasing number of harmonics

Square waves in physical systems have only finite bandwidth and often exhibit ringing effects similar to those of the Gibbs phenomenon or ripple effects similar to those of the σ-approximation.

For a reasonable approximation to the square-wave shape, at least the fundamental and third harmonic need to be present, with the fifth harmonic being desirable. These bandwidth requirements are important in digital electronics, where finite-bandwidth analog approximations to square-wave-like waveforms are used. (The ringing transients are an important electronic consideration here, as they may go beyond the electrical rating limits of a circuit or cause a badly positioned threshold to be crossed multiple times.)


So, either I buy into skin effect, waveguide, blah blah blah, or... I believe this is caused by gear and ears being more sensitive than the pure math shows.

Given those two choices, I pick the latter, simpler version.

The third column is the psychological aspect of expectation.
That is a whole bundle of interesting and confusing stuff.

It is so reassuring to know that the venerable and ever-righteous electricians are willing to take time out of their busy measurements and calculations to instruct we Dionysians on our hearing! I'm sure all thinking audiophiles will agree that we do sometimes listen to things that we shouldn't--image, depth, soundstage, music, etc.--and then act like jerks because the electricians can't hear anything they can't measure. The work of the electricians is indispensable to anyone participating in the audio marketplace and we all need to appreciate their endeavors while we wait for them to find the square root of two.