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Once it has been established that nuclear particles and massive particles as such, as well as what is known as fields, consist of stringy loops of assorted radiuses, it is possible to venture into the phenomena of transverse and longitudinal waves along these strings and within a string system

Any practical experimenting with a string under tension reveals a few observational facts.

• Frequency of a string depends on its tension (see below). Tension applied to a guitar string tunes the string, regulating the frequency of its vibration across a single wavelength. The greater the tension of a string, the higher is its frequency all other criteria preserved.

• Frequency of a string depends on its mass, or better said, its value of inertia. The heavier a guitar string is, the lower is its frequency across a single wavelength, all other criteria preserved.

• Frequency of a string depends on its length. The greater the distance between points of retention of a guitar string, the lower is the frequency of the string across a single wavelength, all other criteria preserved.

• Frequency of a string depends on the speed with which the force was applied to it. Here is the interesting part where force applied across a guitar string(s) of a particular mass range and above a critical speed of application of this force, breaks the common single wave of the string into somewhat complex multiple wave. The frequency of this wave nearly doubles as opposed to the single wave frequency of the same string all other criteria preserved.

The more important observation can be made, when we experiment with the string tension and generator speed relation, needed for breaking of the single guitar wave into a multiple wave. Speed of the force inciting multiple wave must be the higher, the higher is the tension of the string, and may be the slower, the greater the mass of that string. In plain English, the higher is the string tuned, the faster must be the stroke if it is to excite multiple waves on it. This eventually comes to a point, where the tension is so high that any speed of excitation will cause the string to vibrate as a single wave.

It cannot be quite stated that the wave of the string doubles. The single wave is (geometrically) a fairly simple oscillation orthogonal to the string axis. One wave is created strictly between the points of retention. When we achieve to generate a multiple wave, it results in three crests on the string. One crest is the major one in the middle portion of the string and two crests (negative) of approximately half the value of the first one at the sides of the string. In gross terms, it can be stated that the string normal wave value 1 is broken into 1/4-1/2+1/4 waves. The symmetry of inertia (dynamic balance) between the one positive crest and the two negative crests is preserved, but the geometrical symmetry is broken. As the process continues, the two smaller negative crests, being under the longitudinal stress equivalent to that on the larger positive crest, tends to vibrate at roughly double the frequency of the positive crest but is prevented from doing so by the inertial dependency on the positive crest. Therefore, the phenomenon is transient and the wave goes through readily observable (hearable) changes of geometry and eventually settles on a single wave vibration.

The dynamic versus limitation symmetry balances during transition by simultaneous motion of the negative waves toward the center of the string and the whole wave pattern begins to travel back and forth. This all results in further oscillation of the value of tension within the string and this variation can be seen as the cause of timber of the string sound. The whole motion becomes too complex with progression of time to be reasonably described and it is not really necessary. It was necessary to demonstrate that transverse wave of a string under tension has its related longitudinal tension effect, and that it is not possible to separate waves in tense mediums into transverse and longitudinal, as this approach limits the phenomena disregarding some conditions and effects.

It all boils down to plain and simple fact that longitudinal waves create transverse waves and vise versa, as will be further argued.

To allow for still quite simplified understanding of the relations, am going to use a model of a square string network, which can be visualized as a structure of lets say a volleyball net (made of rubber) under even tension in all directions of its plane.

When we slowly pull on any of the net components and then release it, the whole net will start to vibrate as one entity. When we strike the net across a few of its links orthogonally to its plane, so that the inertia of the net does not allow the whole net to accelerate in the direction of excitation at once, we have created transverse wave series across the plane of the net and we have created longitudinal wave series of progressively alternating values of tension through out the plane of the net. Both of these waves propagate to some points of limitation of tension (net posts) and return back toward the point of excitation. The whole system of waves develops into interference of longitudinal and transverse waves. The only way to avoid the interference is to have a round net and excite the wave in its geometric center. Then the wave will diverge and converge in symmetric manner. The first wave generation always diverges in symmetric manner. Only when that wave hits asymmetric framework of retention, it starts interfering.

When we strike a single horizontal thread limited by two knots so fast, that it is released before the force of the strike had time to transfer past the knots, we have generated a single oscillating wave on that thread. Since the points of limitation (knots, with their vertical strings) are not limited within the network by any fixed points, but by “flexible” points, this single eye string wave starts spreading as:

• A traveling transverse wave. This one spreads in the direction of its long axis onto the thread of the same direction in its neighboring eyes in both directions.

• A traveling longitudinal wave of tension variance in the above direction.

When this happens, the original transverse motion of the horizontal string creates orthogonal oscillating tension at its two points of retention (knots), alternately pulling on the vertical strings at these knots. The original longitudinal tension variation of the originally excited horizontal string segment implies a transverse wave on the vertical strings at the knots, generating transverse waves on the vertical strings. The whole process spreads in two orthogonal directions as a combination of transverse and longitudinal waves.

Both, the transverse as well as longitudinal wave within the system, travel at the same speed when interdependent (same as ocean water waves).

The whole pattern of wave relationships develops in due time into a dynamic system of transverse and longitudinal wave system. When the original excitation was achieved exactly in the plane of the net, the whole net will not do much as a whole, as the over all mass of the net can counteract the now chaotic behavior of interference through out the system. When the original excitation has been achieved in any other orientation than the plane of the net, the interference of the individual wave patterns will compound and subtract into larger areas affecting larger portions of the net and inciting transverse waves across quite few eyes of the net. The whole net system will eventually begin wave on a much grander scale than its single eye string components. Should the whole net be resonant by its mass and dimensions to the single eye mass and dimensions, it will vibrate with much less interference than when these two quantity relations are non resonant.

When the knot itself is a relatively heavy object such as a brass weight and the string is excited so that we create a multiple wave on it, its wavelength will not be integral to its length and it will not travel across the knot (brass weight). It will tend to oscillate the knot, but the transfer of its wave activity to the rest of the net will be greatly damped. The wave of such characteristic will oscillate between the points of retention, the knots.

EXPERIMENT

We are being taught that you cannot extract more work or energy from a system than what we put in, disregarding the friction. With friction involved, we cannot do even that much. Well, lets see what an experiment with an oscillating system can do for us.

I have performed one such experiment as a twelve years old rascal. There was a shipyard not far from where I lived and the shipyard had a huge tower crane. The crane was good 50 tons of girded steel (as a structural steel fitter I can do a sensible estimate). It was anchored to stone masonry piers by guy wires. There were, as I recall, 4 or five guy wires. They were made from approximately 2” diameter steel cables and the piers were good 50 to 70 meters from the base of the crane tower. The structure itself was at least 50 meters tall (multiply by 3 for dimensions in feet). The structure was a square based system of four columns and diagonal lattice of trusses with the T of the crane arm at the top.

One of the piers was accessible save for a fence. We went there with my friend on several occasions and it occurred to my friend, one of these times, to see what happens when he kicks the guy wire. Well, it was an interesting experience and we have (quite scientifically) repeated it over and over.

The initial kick created fairly shallow (2”) but long wave on the wire rope. The wave traveled along the rope toward the crane and when it hit the crane, the structure shook a bit and the wave bounced as well as it transferred to the other guy wires and traveled toward their piers. When it hit the piers, each wave reflected and traveled back toward the crane. Then something amazing happened. It looked as if the crane was hit by an earthquake. It shook noisily and violently and swayed back and forth in quite a few directions. In my estimate, I would say it swayed at least 1/4 of a meter off center. The waves bounced again and traveled back to the piers along the guy wires. This time, they were not single waves, but chains of waves. The lengths of the guy wires were obviously not quite the same, and the whole wavy system got “out of tune”, as the next return waves did not perform quite as well as the first returned set did. The periodic shaking of the crane tower diminished with each cycle and the cycles became erratic in time sequence and the whole thing died out.

Any one is my guest to estimate the force with which a kid can kick a steel cable and estimate the force you need to overcome the inertia of a ~ 50T crane tower and see what should be needed to accelerate roughly 2/3 of the 50T tower to sway 1/4m off its axis in something like 1/20 of a second.

Yet, I am far from claiming that small energy will make great deeds, or that the energy, which shook the tower, came from nowhere. I just claim that this energy was by far more than the initial kick put in.

Second effect, which took place in this experiment, was the sound effect. The guitar string made from roughly 2” dia steel wire rope and about 60m long has produced high-pitched noise. This high pitched noise is well above what you get from a guitar high e. Where did it come from? Is it the longitudinal wave within the steel at much higher frequency, therefore speed than the transverse wave was? See SOUND

Anyway, lets have a look at a network, which has the components of my experiment, that is “guy wires” of valence bonds and cranes of nucleuses and molecules and crystals.

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