PiMath.de Planetary Systems of the Earth 1
Classic Systems
  Copyright © Klaus Piontzik  
 German Version    
German Version    

2.4 - Basic oscillations

Now the previous considerations allow a first calculation of a wave that builds up, as the earth, around a sphere. Still, it must be considered that the wave propagation takes place linear and not along the curved surface of the ball.
wave propagation After the Huygens-Fresnel principle the points A, B, C serve so as source points of the standing wave (blue)

Electromagnetic waves propagate
spherically from one point. (red)

If point B is the starting point so the distance BDC = h is the way of the wave.
Illustration 2.4.1 – wave propagation  


Because there is a stationary state, it is sufficient to look at the way of the wave from one source to the next source.
This makes way of the wave
The triangle of MCD in the picture 2.4.1 is rectangular in the point D and apply:
  Sine alpha
Shift the equation to h:
  way of the wave
Since now all sizes are known, the wavelength can be determined:
2.4.1 - Equation: wavelength
In the equation is R the radius of the Earth, n is the number of waves.

This results in the frequency equation for basic oscillations
2.4.2 - Equation: frequency equation n = 1,2,3,4,...
The basic frequency is for n = 1:
2.4.3 - Equation:

basic frequency
basic oscillation
  Illustration 2.4.2 – basic oscillation
This is also the oscillation of a bar with free ends, which length is equal to the diameter of the ball.

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 Planetare Systeme 1

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Der Autor - Klaus Piontzik