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15 - Magnetic layers and frequencies 1

15.1 - Distance consideration

If one looks closer to the distances (from the distance table - chapter 12.2), one recognises they all form multiple of the radius R=6355758,426 m = Lo. This is the basic hull radius. So the distance values can be also shown so:
 
 
  k 1 2 3 4 5 6 7 8
n m                
1 1 Lo 3Lo 5Lo 7Lo 9Lo 11Lo 13Lo 15Lo

 

 

15.2 - Frequency consideration

If one understands the distances l' from the distance table as a wavelength of the accompanying hull respectivly of the oscillation layer, then frequencies can be also assigned to all distances.

 

15.2.1 - Case 1

A possibility exists to orientate by the illustration 6.2. The double diameter is equivalent to the wavelength.
Then it is worth
λ = 4R = 4l' and:
 formula frequency case 1
 
The distance values for n=1 are used from the distance table for the following considerations.
 
  k 1 2 3 4 5 6 7 8  
n m                  
1 1 11,79 3,93 2,358 1,68 1,31 1,07 0,907 0,786 Hz
    6355,76 19067,28 31778,79 44490,31 57201,83 69913,34 82624,86 95336,38 Km
 
It is to be noticed here that for k=2 the half Schumann frequency originates.

 

15.2.2 - Case 2

A farther possibility exists to take the whole diameter of the accompanying hull respectively of the oscillation layer as a wavelength.
So
λ = 2R = 2l' and:
formula frequency case 2
 
 
From the distance table the distance values are used again for n=1.
 
  k 1 2 3 4 5 6 7 8  
n m                  
1 1 23,584 7,861 4,716 3,369 2,62 2,143 1,814 1,572 Hz
    6355,76 19067,28 31778,79 44490,31 57201,83 69913,34 82624,86 95336,38 Km
 
It is to be noticed here that for k=2 the Schumann frequency originates. However, this signifies also that the Schumann frequency is already included in the spectrum of the earth-magnetic frequencies. All appearing frequencies are virtually doublings of the already found basic frequencies so explaining harmonics.

 

15.2.3 - Case 3

For the end here exist still the possibility to interpret the radius of the accompanying hull respectively of the oscillation layer as a wavelength. So λ = R = l' and:
 formula frequency case 3
 
 
From the distance table the distance values are used again for n=1.
 
  k 1 2 3 4 5 6 7 8  
n m                  
1 1 47,17 15,72 9,43 6,74 5,24 4,29 3,63 3,14 Hz
    6355,76 19067,28 31778,79 44490,31 57201,83 69913,34 82624,86 95336,38 Km
 
 
All appearing frequencies are virtually quads of the already found basic frequencies, shows merely harmonics.

 

15.2.4 - Complete reflection

All together the distance and frequency values can be shown for n=1 then as follows:
 
  k 1 2 3 4 5 6 7 8
n m                
1 1 3/2fS 1/2fS 3/10 fS 3/14 fS 1/6 fS 3/22 fS 3/26 fS 1/10 fS
    1/f0 1/3f0 1/5f0 1/7f0 1/9f0 1/11f0 1/13f0 1/15f0
    Lo 3Lo 5Lo 7Lo 9Lo 11Lo 13Lo 15Lo

 

The consequence is that all appearing frequencies in case 1 are representable as rational fraction multiples of certain basic frequencies.
 
In the book the table of the extreme layers from chapter 12.2 is transformed by the described allocation (case 1) to a frequency table.

 

 

15.3 - Earth frequency and Schumann frequency

If one looks closer to the frequencies, a connection can be derived between earth frequency and Schumann frequency.
Easier this succeeds with the frequencies fH2. There exists since a common divisor frequency.
 
For k=1 and k=2 exists a common divisor frequency with:
23,584 = 3 7,861
23,584 = 2 11,792
The frequency 7,861 Hz = fS corresponds to the Schumann freuqency
Then the frequency can be disassembled for k=1, on the other hand, so:
 
23,584 Hz =3fS = 2f0
 
The general relation is (see chapter 15.2 - case 2):
 
 Equation for fh2
 
And from it directly deducible:
 fs = 2/3 fo
 
The Schumann frequency is already included in the spectrum of the earth frequencies

 

From the equation for fH2 is also directly deducible:
 fo = c/4Lo
Furthermore directly deducible:
 fs = c/6Lo
 
The basic hull radius is only a little smaller then the pole or equator radius. Hence, the question arises here which dimensions fS owns if the hull radius is substituted with RA respectively. RP
 
The data of the geodetic reference system WGS84 are:

pole radius: RP= 6356752 m
equator radius: RA= 6378137 m

With
c = 299792458 m/s as the speed of light arises for the single frequencies:
     
For the earth frequencies:    
For the pole radius  fop = c/4Rp = 11,7899 Hz
     
For the equator radius  foa = c/4Ra = 11,7503 Hz
     
For the Schumann frequencies:    
For the pole radius  fsp = c/6Rp = 7,8602 Hz
     
For the equator radius  fsa = c/6Ra = 7,8339 Hz

 

Noteworthy here is still the fact that the Schumann frequency, for historical reasons, is won from a cavity resonator consideration. (see in addition chapter 7.1)
The concurrent derivation from the earth frequency, so, in the end, from the radii of the earth, shows that the measurements of this planet and the generated frequencies on it stands in a closed connection.

 

 

15.4 - An approximation for the equator frequencies

If one takes, in the geophysical sciences usual, middle radius of 6,371 km, one receives for fS a value from 47,0558 hertz. This lies near with 47 hertz.
If one calculates on 47 hertz back, the radius arises to 6,378,563 km. This is about 400 metres bigger than the equator radius. Approximately one can say:
 
47 Hz =6fS = 4f0
 
From it arises:
 
fS = 47:6 Hz = 7,8333... Hz
f0 = 47:4 Hz = 11,75 Hz
 
This can be used as a good approximation for the equator radius frequencies.

 

 

15.5 - Common frequencies

A general connection can be derived by the equation from chapter 15.3 still between earth frequency and Schumann frequency.
The relation
f0/3 = fS/2 is preserved also if one multiplies the equation by a rational number, so to a fraction. With it arises in general:
 
 Equation for the common frequencies
 
n and k are elements of the natural numbers (1, 2, 3, 4...)
 
A complete spectrum of common frequency fos originates from the equation, so that the earth frequency and the Schumann frequency stand with each other in a functional connection.

Systematic using of the parametres
n and k in the equation leads to a table in which then all common frequencies are included.
The calculation of the table values occurs about the corrected basic frequency from
chapter 11.2. A rounded value from fo = 11,792 Hz is used.

common frequencies for n<17, k<9

k 1 2 3 4 5 6 7 8  
n                  
1 3,9307 1,9653 1,3102 0,9827 0,7861 0,6551 0,5615 0,4913 Hz
2 7,8613 3,9307 2,6204 1,9653 1,5723 1,3102 1,123 0,9827 Hz
3 11,792 5,896 3,9307 2,948 2,3584 1,9653 1,6846 1,474 Hz
4 15,7227 7,861 5,2409 3,9307 3,1445 2,6204 2,2461 1,9653 Hz
5 19,6533 9,8267 6,5511 4,9133 3,9307 3,2756 2,8076 2,4567 Hz
6 23,584 11,792 7,8613 5,896 4,7168 3,9307 3,3691 2,948 Hz
7 27,5147 13,7573 9,1716 6,8787 5,503 4,5858 3,9307 3,4393 Hz
8 31,4453 15,7227 10,4818 7,8613 6,2891 5,2409 4,4922 3,9307 Hz
9 35,376 17,688 11,792 8,844 7,0752 5,896 5,0537 4,422 Hz
10 39,3067 19,6533 13,1022 9,8267 7,8613 6,5511 5,6152 4,9133 Hz
11 43,2373 21,6187 14,4124 10,8093 8,6475 7,2062 6,1768 5,4047 Hz
12 47,168 23,584 15,7227 11,792 9,4336 7,8613 6,7383 5,896 Hz
13 51,0987 25,5493 17,0329 12,7747 10,2197 8,5164 7,2998 6,3873 Hz
14 55,0293 27,5147 18,3431 13,7573 11,0059 9,1716 7,8613 6,8787 Hz
15 58,96 29,48 19,6533 14,74 11,792 9,8267 8,4229 7,37 Hz
16 62,8907 31,4453 20,9636 15,7227 12,5781 10,4818 8,9844 7,8613 Hz

 

Besides, the first smallest natural frequency is fo/3 = fs/2 = 3,9307 Hz that earth frequency and Schumann's frequency own together.
The table with the common frequencies also contains all harmonics of the Schumann frequency. With it the Schumann spectrum (from
chapter 7) belongs to the frequency spectrum of the table 46. I.e. the whole Schumann spectrum can be derived from the earth frequency.

 

 

15.6 - The sferic frequencies

Another connection from the equation of chapter 15.5 arises if bigger n, so higher frequency, are looked:

common frequencies for 1055<n<12673, k<9

k 1 2 3 4 5 6 7 8  
n                  
1056 4150,784 2075,392 1383,595 1037,696 830,157 691,797 592,969 518,848 Hz
1584 6226,176 3113,088 2075,392 1556,544 1245,235 1037,696 889,454 778,272 Hz
2112 8301,568 4150,784 2767,189 2075,392 1660,314 1383,595 1185,938 1037,696 Hz
2640 10376,96 5188,48 3458,987 2594,24 2075,392 1729,493 1482,423 1297,12 Hz
3168 12452,35 6226,176 4150,784 3113,088 2490,47 2075,392 1778,907 1556,544 Hz
7128 28017,79 14008,89 9339,264 7004,448 5603,558 4669,632 4002,542 3502,224 Hz
12672 49809,41 24904,7 16603,14 12452,35 9961,882 8301,568 7115,63 6226,176 Hz

 

The spectral maxima of the sferic frequencies are given in general, as follows in very much narrow-banded areas
(see "Sferics" by Hans Baumer page 285):
 
4150,84 Hz - 6226,26 Hz - 8301,26 Hz - 10377,10 Hz - 12452,52 Hz - 28018,17 Hz - 49810,08 Hz
 
The comparison of the Sferic spectrum with the table values delivers a good correspondence of the values. About the whole spectrum seen the maximal mistake lies less than 0.7 hertz.
In his book " the cosmic octave " (page 39) produces Cousto a connection between Sferic frequency and sidereal day. The comparison with the earth rotation delivers a minimum difference of about 3 hertz and grows with increasing frequency up to a maximum value of about 36 hertz. The increasing difference clearly shows that the frequency calculation about the sidereal day only is suited as an approximate value.
As by the equation from chapter 15.5 and the generated table for 1055<n<12673 have been shown that the Sferic frequencies, with enough exactness, are included in the spectrum of the common earth frequencies and Schumann frequencies.

 

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