 The magnetic field of the earth Lattice structures of the earth magnetic field Impressum Copyright © Klaus Piontzik German Version

6 - Derivation of the wavelength

6.1 - Conditions

 The basic condition after chapter 5.2 is that a whole number of oscillations fits once around the earth and thus forms a standing wave, as a steady state. In a first attempt counts to the surface: Wavelength = circumference/number of oscillations The wavelength corresponds to a certain distance on the circumference of the earth. In the following illustration 6.1 the situation is illustrated for an oscillation. Both points A and C are the end points of the circular arc s, which is at the same time also a wavelength l and If one looks at this situation from the earth centre, a certain angle a can be assigned to every oscillation. Then all together as a basis appears: For reasons of the illustration a factor has remained unnoticed, in the previous representation, which must be included now in the consideration: the ball figure of the earth. It must be still taken into consideration that the wave propagation linearly takes place, and not along the curved earth surface. Hence, in the consequence it requires a modification of the basic equation. Illustration 6.1 - Wavelength and circumference

6.2 - The derivation

 After the Huygens principle the points A, B, C in Illustration 6.1, so the extreme points, serve as source points of the standing wave. Electromagnetic waves spread out spherically from a point and if point B is the starting point, corresponds the distance BDC = h to the way of the wave. Because there is a steady state and it is enough to look the way of the wave from a source to the next source. The triangle MCD is right-angled in the point D and it counts:  Change after lambda dash produces the corrected wavelength: 6.3 - The frequency equation

 The connection between wavelength and frequency is: With thus arises the equation for the earth frequencies: c stands for the speed of light, R for the radius of the earth, n n for the number of oscillationsBecause the earth is, however, no perfect sphere, there to the poles flattened. Here exist two radii: the pole radius and the equator radius. And from it also result two (easily divergent of each other) basic frequencies. The geodetic reference system WGS84 is based on a spheroid, so to a rotation ellipsoid. See in addition chapter 17.1. The data of the geodetic reference system WGS84 are: Pole radius : 6356752 m Equator radius : 6378137 m Flattening : 1:298,2572 With c = 299792458 m/s as the speed of light arises with n=1 for the single radii: Pole radius : 11,79 Hertz Equator radius : 11,75 Hertz The appearing difference may seem unimportant at first sight. However, in case of farther consideration a significant difference arises. In the next chapter 7 this will become still clearly recognizable in the subject sferics. Remark: Nikolas Tesla declared at his time that the earth frequency lies near 12 hertz.

6.4 - A relation to the pole axis of the earth

 Another connection to the pole axis is given by the basic oscillation. If one declares for the first basic frequency the general solutions, these are:
 n f Pole radius Equator radius 1 11,79 Hz 11,75 Hz 2 16,674 Hz 16,618 Hz 3 23,58 Hz 23,5 Hz
 For n=1 the general equation for the wavelength is: lambda = 4R And one receives the identical result if a rod of the length of the Pole axis freely swung at both ends. As well as in the following illustration 6.2 shown. Illustration 6.2 - Earth and basic oscillation Here the analogy is a massive rod which both ends are free. If this rod is moved now into oscillation, the basic oscillation starting longitudinal flexural vibration corresponds to the picture 6.2. (see also „Physik“ von Gerthsen, Kneser, Vogel – Kapitel 4.1.5)

6.5 - The frequencies of the earth

 If one puts successively for n the values 1,2.3 ... in the above equation for the frequency, the basic frequencies of the earth arises. The following table contains the first 30 frequency oriented on the pole radius.

 n Pole radius 1 11,7903 Hz 2 16,6740 Hz 3 23,5806 Hz 4 30,8095 Hz 5 38,1542 Hz 6 45,5542 Hz 7 52,9850 Hz 8 60,4350 Hz 9 67,8975 Hz 10 75,3688 Hz 11 82,8465 Hz 12 90,3289 Hz 13 97,8149 Hz 14 105,3038 Hz 15 112,7949 Hz 16 120,2880 Hz 17 127,7825 Hz 18 135,2783 Hz 19 142,7752 Hz 20 150,2730 Hz 21 157,7715 Hz 22 165,2708 Hz 23 172,7706 Hz 24 180,2709 Hz 25 187,7717 Hz 26 195,2729 Hz 27 202,7744 Hz 28 210,2762 Hz 29 217,7784 Hz 30 225,2807 Hz

 To this basic frequency suitable harmonivs still appear, i.e. one must form in addition only the integer multiples. (One calls harmonics as general integer multiples of an elective basic frequency) In the book the frequencies are still declared which are oriented on the equator radius.

6.6 - A further derivation

 In the book the derivation is still declared for a farther frequency equation.  back home next The book to the website - The website to the book at time is the book only in german language available buy on Amazon in over 1000 Online Shops Production and Publishing company: Books on Demand GmbH, Norderstedt ISBN 9-783833-491269 Store price: 35 Euro 380 sides 72 pictures of it 51 in colour 55 tables 1530 literature references 1900 entries in the register of names

 The theory, which is developed in this book is based on the remake and expansion of an old idea. It was the idea of a central body, preferably in the shape of a ball, formed around or in concentric layers. Democritus was the first who took this idea with his atomic theory and thereby introduced himself to the atoms as fixed and solid building blocks. Is the atom used as a wave model, that allows to interpret concentric layers as an expression of a spatial radial oscillator so you reach the current orbital model of atoms. Now, this book shows that these oscillatory order structures, described by Laplaces equation, on earth and their layers are (geologically and atmospherically) implemented. In addition the theory can be applied on concentric systems, which are not spherical but flat, like the solar system with its planets, the rings that have some planets and the moons of planets or also the neighbouring galaxies of the milky way. This principle is applicable on fruits and flowers, such as peach, orange, coconut, dahlia or narcissus. This allows the conclusion that the theory of a central body as a spatial radial oscillator can be applied also to other spherical phenomena such as spherical galactic nebulae, black holes, or even the universe itself. This in turn suggests that the idea of the central body constitutes a general principle of structuring in this universe as a spatial radial oscillator as well as macroscopic, microscopic and sub microscopic. buy on Amazon