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Stability, Directionality and Conclusion

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To illustrate how little internal movement occurs, we will look at a 10 AWG wire that at 0.102 in (0.259 cm) diameter is rated to carry a current (I) of 30 amps. With a 0.040 inch PVC insulator and a 0.040 in (0.102 cm) jacket around a twisted pair configuration, the nominal outside diameter (d) of the wire and insulation is 0.182 in (0.462 cm) which also equals the center to center separation of the wire pair. Using these numbers, we can calculate the force of one wire against the second when current flow in opposite directions, which causes repulsion.

Magnetic Field: = 0.00130 T; mu o

Force per length: = 0.0390 N/m

The amount of movement that will be produced by these two wires constrained in a jacket can be determined from the equations for a cylindrical pressure vessel. If we assume that there is a sufficient twist pitch that the forces generate an average uniform force outwards in all directions we can calculate the approximate increase in size of the jacket. The inside diameter of the jacket will be 2d = 0.924 cm with a circumference of 2.903 cm, which gives an internal pressure:


The radial expansion can be calculated from the internal pressure (p) on a cylinder of known thickness (b = 0.102 cm), radius (r = 0.513 cm to mid thickness), and elastic modulus (for extruded PVC E = 0.00179 to 4.83 GPa). If we use the lower bound of E = 1790000 Pa, we get the following increase to the radius:


The diameter increases by 38.8 nm, which is an order of magnitude smaller than the lower bound wavelength of ultraviolet light at 280 nm. Not very much movement at all, one might even say insignificant.

To illustrate how little external movement occurs from acoustic transmission, we will look at a very high pressure change. Using values from our previous example of internal movement from electromagnetic forces, we will look at a 30 Pa acoustic pressure change, which is just over 120 dB, to calculate the amplitude of the air movement using the speed of sound in air at c = 343.2 m/s and the density of air at 20oC, air has a displacement amplitude based on the characteristic impedance of air:

eqn characteristic impedance of air



For a frequency of 20 Hz, the amount of movement of a wire in its own electric field will produce movement of only 0.58 mm and 20 kHz of only 0.58 . The velocity of air particles when they displace is:


The particle velocity is a constant with frequency as this term cancels out. As a simplification, if we assume that the cable moves at the rate of the surrounding air with only a phase lag, the velocity of the 12’-0” wire will produce an emf voltage in the speaker cable:


As an upper bound solution, we have an addition of three thousandths of a dBV to the signal, not very much at all.

Then we have another misused engineering term, stability, which is not the same as stiffness, as implied here by speaking of preventing movement.

Mechanical Stability
The ANJOU Speaker Cable has been meticulously designed to minimize physical movement within the cable.

The ANJOU Speaker cable has been designed to have exceptional strength and stability, requiring large amounts of force to create any movement.

Various, Pear Cable: Anjou Speaker Cable

Stability as a mathematical concept is the sensitivity of a function to small perturbations. A stable system will not undergo disproportionate change in response to the perturbation.

The concept is applied in engineering mechanics to consider how difficult it is to displace material from a state of equilibrium. In solid mechanics, an object is unstable if a slight load increase or movement causes unbounded deformation. Such a system is on the verge of collapse with the loss of load bearing capacity known as buckling or instability.

The levels of acoustic and electromagnetic forces that occur in any speaker cable design are not about to cause the cable to go flopping around the listening room or even cause the individual conductors to go flopping around inside the outer jacket through either a loss of mechanical stability or resonant behavior.

Incidentally, if the cables did actually have any sort of exceptional stiffness to prevent movement, one would be hard pressed to bend the cables around the back of amplifiers and speakers to a make connection. This is just another exaggeration I’m afraid.

Pear then states a need for internal cable damping, which assumes there is a mechanical resonance issue. Resonance only occurs at specific frequencies, known as modes, and each modal harmonic is increasingly less significant. It is well known from vibration theory that if there is a not significant energy input from a frequency near a resonant peak that damping does nothing.

Pear is also worried about cable movement relative to connectors, but any well made termination will eliminate movement and any potential for noise:

The only other thing that is important is that the cables are properly terminated so they don't become noisy, and that the shield is of good quality and provides complete protection from external interfering signals. Terminations will normally be either soldered or crimped, and either is fine as long as it is well made. For the constructor, soldering is usually better, since proper crimping tools are expensive.

The Truth About Interconnects and Cables

Differential length is just not important, as there is certainly more variation in distance between the listener’s ears and each speaker than the fractional inch differences in wire length. When one considers that sound in air travels at 1130 ft/s is many orders or magnitude slower than electricity in a copper wire which approaches the speed of light at 42-72% of c (c = 983,571,056 ft/s), the differences will be exaggerated even further. For a 100 ft difference in cable length at .42c verses a 1 ft difference in ear location:

Wire:

Air:

Calculations provided by Audioholics have previously shown signal loss in 50ft of 12AWG standard zip cord to be less than 1 dB at 20 kHz and group delay of 209 ns = 209x10-9seconds, which is six orders of magnitude smaller than 5x10-3 seconds that a human can hear only under optimal test conditions.

As far as high frequency attenuation, the 1 ft difference in relative ear location does not even get into the off axis high frequency attenuation due to the speakers. Any differences in the angle of each ear relative to each speaker axis, that likely accompanies the difference in ear position, will be far more detrimental than any attenuation from different cable lengths.

Cable directionality is a complete fabrication, especially when considering the cyclic nature of AC:

Your ANJOU interconnects are marked with directional arrows that indicate the direction that the conductors were drawn in. This is primarily a result of general engineering practices to control as many variables as possible. Some people feel that the cables sound better when the cables are aligned with the directional arrows with the “direction” of the signal. It is important to remember that the audio signal is fundamentally AC and thus the electrons are moving both forward and backward. The final word on this subject is that Pear Cable recommends hooking up the cables following the directional arrows. This recommendation is based on the simple principle of controlling as many variables as possible.

Pear FAQ 5: Are ANJOU interconnects directional?

Here is another mechanics error: drawn wire will have no longitudinal variation in properties and is unaffected by which end is held in place and which end is pulled. Relative to the metal that is being drawn, a Free Body Diagram of the forces involved will show an equal an opposite force at both ends consistent with Newton’s Laws of Motion; basic mechanics. Relative to the wire, both ends are pulled equally so there is no variable to control. This problem is an elementary topic that should be readily identifiable and solvable to any second year engineering student.

Finally, another Audioholics favorite, audio cable break in:

You may listen to your cables directly out of the box and get most of the performance immediately. However, it will take approximately 1 day for the cables to mechanically settle after they have been moved or set up for the first time, which can have an effect on the sound. Some users do report a need for our cables to "break in" over time to achieve the optimum performance. Customers must make their own decision as to how long is necessary to "break in" the cables, but do not hesitate to listen to them immediately.

Pear FAQ 8: Do I need to “Break-In” my cables?

The statement that cables mechanically settle is utter BS but let’s entertain two possibilities.

The only place one will see settlement published as a recognized engineering term is as a phenomenon in soil mechanics and foundation engineering. It occurs when a significant change in load is applied to soil, which causes consolidation of the soil where water is squeezed out, decreasing the soil volume. Such an event should not occur in speaker cables.

The other possibility is that if by settlement the phenomenon of creep is implied by this improper terminology, it is also a non-issue for audio. Creep occurs when a material is loaded and the deformation increases over time with no change in load, resulting in microscopic volumetric and density changes. Many polymers do exhibit creep but metals do not exhibit any significant creep. Moving speaker cables is unlikely to cause any significant creep, and even implying that such would be a source for cable break in would mean that any time a cable was relocated it would again require brake in. Audiophiles claim to hear break in only when cables are new, not when they have relocated cables they have owned longer than the supposed initial break in.

In closing, there are numerous stories of believers in magic cables being caught hearing what they want, not what is present to be heard:

John Dunlavy, who manufactures audiophile loudspeakers and wire to go with it, does think questioning is valid. A musician and engineer, Mr. Dunlavy said as an academic exercise he used principles of physics relating to transmission line and network theory to produce a high-end cable. "People ask if they will hear a difference, and I tell them no," he said.

Mr. Dunlavy has often gathered audio critics in his Colorado Springs lab for a demonstration.

"What we do is kind of dirty and stinky," he said. "We say we are starting with a 12 AWG zip cord, and we position a technician behind each speaker to change the cables out." The technicians hold up fancy-looking cables before they disappear behind the speakers. The critics debate the sound characteristics of each wire. "They describe huge changes and they say, 'Oh my God, John, tell me you can hear that difference,'" Mr. Dunlavy said. The trick is the technicians never actually change the cables, he said, adding, "It's the placebo effect."

A Spat Among Audiophiles Over High-End Speaker Wire

Roy Furchgott, The New York Times

From: The Truth About Interconnects and Cables

Mr. Dunlavy has made similar criticisms about the claims of exotic cable manufacturers on other occasions as well. Cable magic is nothing but the placebo effect.

Engineering Judgment

Good engineering judgment is based on the knowledge and experience that distinguishes good engineering from poor. Knowing what constitutes a significant design parameter to consider and what does not is crucial. Poor engineering judgment leads to flawed designs that do not solve the intended problems or are unnecessarily expensive. Diminishing returns, a fundamental principle of modern economics, weighs heavily on any extreme design. A good engineer recognizes this fact and uses engineering judgment to consider the significance of the factors and designs only for the ones that matter in order of relative importance.

For $302 per foot, Pear Cable has not shown proof that they can provide any significant audible improvements that justify the cost. As illustrated in this discussion using established engineering and scientific knowledge, the significance of the design parameters that Pear considers important are easily questioned, leaving the onus of proof on Pear to prove their designs and not the other way around as Pear has suggested.

In addition to the insignificant effect that cable has to the overall system performance, numerous other factors that further trivialize the significance of speaker wire and interconnect on audio performance:

    • Limits of the quality of the original recording and recording equipment
    • Limits of circuit traces and internal wiring quality in the reproduction electronics
    • Other gear you could buy for seven thousand dollars

If in fact, the Anjou cables do cost as much as claimed to engineer and manufacture, there is a significant waste of engineering effort and manufacturing resources to accomplish very little if anything.

The challenge by the JREF was an opportunity for Pear to prove the significance of the design parameters that they deem important and that they believe in their product.

Pear Cable has the utmost confidence in the products that we offer, and the products have all had their scientific principles verified by human listening. We can stand behind all of the design principles that we utilize; can the other guys do that?

Pear Cables: FAQ number 2

Instead, Pear has chosen to avoid having the significance of their scientific principles verified by human hearing under controlled, scientific circumstances in public which only serves to put their integrity further into question.

Conclusion: So What Does $7250 Buy?

Cables are simply electrical wave guides to transmit signal between audio components. While cables do posses electrical properties that interact within a circuit, those properties are generally insignificant to those of other system components when properly designed. A properly designed cable should cause minimal signal loss and have no effect on the balance of frequency content in the signal, which simply means a flat frequency response. Cables that can not do this degrade the sound quality, irrespective of their cost.

As a case study, we have put a single company under the microscope to illustrate how to identify many of the fallacies promulgated by exotic cable manufacturers. All of the issues that have been brought up in this discussion are equally valid for any audio cable manufacturer that makes these claims. An analysis such as this can and should be performed on any product manufacturer that charges an exorbitant or disproportionate amount of money for a simple product that comes with claims of equally disproportionate benefits or improvements.

While dissecting marketing BS posing as scientific proof and engineering design casts a very long shadow over the credibility of a product manufacturer when there is a clear misuse of scientific principles, it is not direct proof that an actual design does not work as claimed; for that, we will turn to experimental testing. Based on the only testing supplied by Pear Cable, the anonymous frequency response plot, we ask the $7250/12 ft pair question:

What does $7250 for speaker cables really buy?

It buys a very expensive filter.

References

 

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Recent Forum Posts:

Clint DeBoer posts on May 13, 2008 15:52
Never let is be said that our reviewers can't take a hit. lol
AdrianMills posts on May 13, 2008 13:23
David Waratuke, post: 411992
Nope, just clearing up some misinformation suggested in one of the posts.

Appearantly I was unaware of how touchy a subject ham radio is for the operators. There were a lot more unhappy feelings in some of the posts than I would have expected for such a minor mention of the topic for a percieved slighting that was certainly not intentional.

David

Welcome to the WWW.
DavidW posts on May 13, 2008 13:19
Clint DeBoer, post: 411867
Oh my gosh, David - give it a rest will you. Last time I checked, the point of the article wasn't to insult Ham Radio operators.

Please send me some recommended changes and go find something else to defend your honor on.

Nope, just clearing up some misinformation suggested in one of the posts.

Appearantly I was unaware of how touchy a subject ham radio is for the operators. There were a lot more unhappy feelings in some of the posts than I would have expected for such a minor mention of the topic for a percieved slighting that was certainly not intentional.

David
Clint DeBoer posts on May 13, 2008 12:54
Article updated with submission from David… Red chicklets given to David, lol
gene posts on May 13, 2008 10:48
Oh my gosh, David - give it a rest will you. Last time I checked, the point of the article wasn't to insult Ham Radio operators.

Please send me some recommended changes and go find something else to defend your honor on.

Agreed this is simply ridiculous. Make the necessary corrections ASAP. thanks.
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