02 Jan 2022. Observations; More About Modes.
1602 Jan 2022. Observations. More About Modes.
We are discussing what the Modes are, relative to measuring Schumann resonances.
The modes are what give the colouring to the spectrogram; but what are "modes", relative to SR ?
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Mode. In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave state of excitation, in which all the components of the system will be affected sinusoidally at a fixed frequency associated with that mode.
In an electrical dynamical system, a resonant cavity made of thin metal walls, enclosing a hollow space, for a particle accelerator is a pure standing wave system, and thus an example of a mode, in which the hollow space of the cavity is the medium, the RF source (a Klystron or another RF source) is the excitation and the electromagnetic field is the modal variable.
When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones".
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Mode numbers. A mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of half waves in the vibration. For example, if a vibrating beam with both ends pinned displayed a mode shape of half of a sine wave (one peak on the vibrating beam) it would be vibrating in mode 1. If it had a full sine wave (one peak and one trough) it would be vibrating in mode 2.
In a system with two or more dimensions, such as the pictured disk, each dimension is given a mode number. Using polar coordinates, we have a radial coordinate and an angular coordinate. If one measured from the center outward along the radial coordinate one would encounter a full wave, so the mode number in the radial direction is 2. The other direction is trickier, because only half of the disk is considered due to the anti-symmetric (also called skew-symmetry) nature of a disk's vibration in the angular direction. Thus, measuring 180° along the angular direction you would encounter a half wave, so the mode number in the angular direction is 1. So the mode number of the system is 2–1 or 1–2, depending on which coordinate is considered the "first" and which is considered the "second" coordinate (so it is important to always indicate which mode number matches with each coordinate direction).
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A standing wave is a continuous form of normal mode. In a standing wave, all the space elements (i.e. (x, y, z) coordinates) are oscillating in the same frequency and in phase (reaching the equilibrium point together), but each has a different amplitude.
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Aronmix timestamps:
15:47 - 24:51
54:21 - 1:07:32
1:20:20 - 1:32:41
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Normal mode: ( https://en.wikipedia.org/wiki/Normal_mode )
Standing waves: ( https://en.wikipedia.org/wiki/Normal_mode )
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