Chladni figures- Standing waves /stehende Wellen

Roman Chijner, leucotea, May 16, 2017

Table of Contents

  1. Weblinks, videos, pictures
    1. Weblinks, videos, images
    2. Bilder zu Stehwelle
    3. Chladnische Klangfigur
    4. Moiree-01-05
    5. Moiree-11-15
    6. Moiree-Effekt: Zufallsraster
  2. cross section plotter: 2D and 3D Standing waves
    1. Querschnittsplotter für 2D Chladni Figuren
    2. Querschnittsplotter für 3D Chladni Figuren
    3. Querschnittsplotter für 3D Chladni Figuren
    4. Video: 2D und 3D Chladni Figuren in Querschnittsplotter
    5. Chladni Plate Animation
  3. spacial Chladni patterns/ räumliche Chladni Figuren
    1. Video: spacial Chladni patterns/ räumliche Chladni Figuren
    2. Spacial Chladni patterned surfaces  as a network of lists of points
    3. Spacial Chladni patterned surfaces  as a network of implicit curves
    4. Spacial Chladni patterned surfaces  as a network of implicit curves
  4. pictures: spacial Chladni patterns
    1. gallery 1 →Chladni Figuren
    2. gallery 2 →Chladni Figuren
  5. Some earlier versions of "Chladni" applets
    1. Implicit surfaces as a network of implicit curves
    2. spacial Chladni patterns/ räumliche Chladni Figuren
    3. Räumliche Chladni Figuren- 1 2 6, s=1, L=20 HSVRGB.ggb
    4. Räumliche Chladni Figuren-1 3 4, s= -1, L=20
    5. Räumliche Chladni Figuren- 1 3 4, s=1, L=20
    6. Räumliche Chladni Figuren- 1 2 3, s=-1, L=20
    7. Räumliche Chladni Figuren-1 3 4, s= 1, L=20
    8. Räumliche Chladni Figuren- 2 3 5, s=-1, L=20
    9. Rräumliche Chladni Figuren- 1 2 3 ,s=1, L=20
    10. Räumliche Chladni Figuren- 2 3 5, s=1, L=20
    11. Räumliche Chladni Figuren 1 3 5, s=1, L=20
    12. 3D-stehende Wellen (räumliche Chladni Figuren)
    13. 3D-stehende Wellen (räumliche Chladni Figuren) 1 2 3
    14. 3D-stehende Wellen (Chladni Figuren)
    15. 3D-stehende Wellen ("räumliche Chladni Figuren")
    16. 3D-stehende Wellen ("räumliche Chladni Figuren")
    17. listenweise and punktweise Trace- Methode (HSV Färbung)
    18. listenweise and punktweise Trace- Methode (HSV Färbung)
    19. spacial Chladni patterns

1.

Weblinks, videos, pictures

  • 1. Weblinks, videos, images
  • 2. Bilder zu Stehwelle
  • 3. Chladnische Klangfigur
  • 4. Moiree-01-05
  • 5. Moiree-11-15
  • 6. Moiree-Effekt: Zufallsraster

1.1.

Weblinks, videos, images

Weblinks
[size=85][url=http://paulbourke.net/geometry/chladni/][color=#666666][u]http://paulbourke.net/geometry/chladni/[br][/u][/color][/url][url=http://www.phy.davidson.edu/stuhome/jimn/chladni/pages/theory.htm][color=#6161ff][u]http://www.phy.davidson.edu/stuhome/jimn/chladni/pages/theory.htm[/u][/color][/url][br][url=http://www.cymascope.com/cyma_research/physics.html]http://www.cymascope.com/cyma_research/physics.html[br]https://www.youtube.com/watch?v=Q3oItpVa9fs[/url][br][url=http://www.odinic-rite.org/main/harmonic-vibrations/]http://www.odinic-rite.org/main/harmonic-vibrations/[/url][br] [url=http://sploid.gizmodo.com/these-images-of-sound-waves-in-water-are-hypnotic-1759741538]http://sploid.gizmodo.com/these-images-of-sound-waves-in-water-are-hypnotic-1759741538[br][/url][url=http://www.cymascope.com/cyma_research/breakingnews.html]http://www.cymascope.com/cyma_research/breakingnews.html[br]https://www.youtube.com/watch?v=XBP0jmpjzBw[/url][/size]
[size=85]https://acousticslab.org[br] https://acousticslab.org/RECA220/PMFiles/Module01.htm[br]https://acousticslab.org/RECA220/PMFiles/Module02a.htm[br]https://acousticslab.org/RECA220/PMFiles/Module02b.htm[br]https://acousticslab.org/RECA220/PMFiles/Module03.htm[/size]
Chladni Patterns
Three-Dimensional Mid-Air Acoustic Manipulation [Acoustic Levitation]
Cymatic Music
Cymatics Experiment Mozart "Una Donna a Quindici Anni" Suzanne Tribe Suzanne Tribe
3-Dimensional Standing-Wave Patterns in Liquid picture
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Images of Sound Waves in Water
http://sploid.gizmodo.com/these-images-of-sound-waves-in-water-are-hypnotic-1759741538
The Physics of Sound
[url=http://www.cymascope.com/iphoneweb/cymaphone/cyma_research/physics.html]http://www.cymascope.com/iphoneweb/cymaphone/cyma_research/physics.html[/url][br][br][url=https://www.academyofeuphony.com/en/cymascope-music-made-visible/]https://www.academyofeuphony.com/en/cymascope-music-made-visible/[/url]
Holographic Music
Cymatics, shamanic drums
[url=http://www.massey.ac.nz/massey/learning/colleges/college-of-sciences/research/natural-mathematical-sciences/physics-research/musical-vibration-patterns-and-ultra-cold-atoms/musical-vibration-patterns-and-ultra-cold-atoms_home.cfm?stref=666930]http://www.massey.ac.nz/massey/learning/colleges/college-of-sciences/research/natural-mathematical-sciences/physics-research/musical-vibration-patterns-and-ultra-cold-atoms/musical-vibration-patterns-and-ultra-cold-atoms_home.cfm?stref=666930[/url]
[url=http://www.massey.ac.nz/massey/learning/colleges/college-of-sciences/research/natural-mathematical-sciences/physics-research/musical-vibration-patterns-and-ultra-cold-atoms/musical-vibration-patterns-and-ultra-cold-atoms_home.cfm?stref=666930]http://www.massey.ac.nz/massey/learning/colleges/college-of-sciences/research/natural-mathematical-sciences/physics-research/musical-vibration-patterns-and-ultra-cold-atoms/musical-vibration-patterns-and-ultra-cold-atoms_home.cfm?stref=666930[/url]
– Roman Chijner

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

cross section plotter: 2D and 3D Standing waves

  • 1. Querschnittsplotter für 2D Chladni Figuren
  • 2. Querschnittsplotter für 3D Chladni Figuren
  • 3. Querschnittsplotter für 3D Chladni Figuren
  • 4. Video: 2D und 3D Chladni Figuren in Querschnittsplotter
  • 5. Chladni Plate Animation

2.1.

Querschnittsplotter für 2D Chladni Figuren

Die Gleichung für die Nullstellen der Stehwelle auf einer quadratischen Chladnischen Platte (mit Seitenlänge L) wird durch das folgende gegeben:[br]cos(n pi x / L) cos(m pi y / L) +s*cos(m pi x / L) cos(n pi y / L) = 0,[br]wobei n und m ganze Zahlen sind, s=∓1. [br]Das ist eine Verallgemeinerung "Chladni Plate Mathematics, 2D", Written by Paul Bourke: http://paulbourke.net/geometry/chladni/[br]Zugang zu den ggb files auf: http://www.umtriebe.de/3D_anwendungen.html[br]video: https://www.youtube.com/watch?v=F9fCumuIcbQ
– Roman Chijner

2.2.

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2.3.

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2.4.

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2.5.

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3.

spacial Chladni patterns/ räumliche Chladni Figuren

  • 1. Video: spacial Chladni patterns/ räumliche Chladni Figuren
  • 2. Spacial Chladni patterned surfaces  as a network of lists of points
  • 3. Spacial Chladni patterned surfaces  as a network of implicit curves
  • 4. Spacial Chladni patterned surfaces  as a network of implicit curves

3.1.

Video: spacial Chladni patterns/ räumliche Chladni Figuren

– Roman Chijner

3.2.

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3.3.

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3.4.

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4.

pictures: spacial Chladni patterns

  • 1. gallery 1 →Chladni Figuren
  • 2. gallery 2 →Chladni Figuren

4.1.

gallery 1 →Chladni Figuren

Chladni Figuren- 1 2 4, s=1, L=20 39-46
Chladni Figuren- 1 2 5, s=1, L=20 44-50
Chladni Figuren- 1 2 6, s=1, L=20 39-44
Chladni Figuren- 1 2 6, s=1, L=20 46-50
Chladni Figuren- 1 2 7, s=1, L=20 6-15
Chladni Figuren- 1 2 7, s=1, L=20 35-39
Chladni Figuren- 1 2 8, s=1, L=20 01-15
Chladni Figuren- 1 2 8, s=1, L=20 29-33
Chladni Figuren- 1 2 9, s=1, L=20 43-50
Chladni Figuren- 1 3 5 i=48-50
– Roman Chijner

4.2.

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5.

Some earlier versions of "Chladni" applets

  • 1. Implicit surfaces as a network of implicit curves
  • 2. spacial Chladni patterns/ räumliche Chladni Figuren
  • 3. Räumliche Chladni Figuren- 1 2 6, s=1, L=20 HSVRGB.ggb
  • 4. Räumliche Chladni Figuren-1 3 4, s= -1, L=20
  • 5. Räumliche Chladni Figuren- 1 3 4, s=1, L=20
  • 6. Räumliche Chladni Figuren- 1 2 3, s=-1, L=20
  • 7. Räumliche Chladni Figuren-1 3 4, s= 1, L=20
  • 8. Räumliche Chladni Figuren- 2 3 5, s=-1, L=20
  • 9. Rräumliche Chladni Figuren- 1 2 3 ,s=1, L=20
  • 10. Räumliche Chladni Figuren- 2 3 5, s=1, L=20
  • 11. Räumliche Chladni Figuren 1 3 5, s=1, L=20
  • 12. 3D-stehende Wellen (räumliche Chladni Figuren)
  • 13. 3D-stehende Wellen (räumliche Chladni Figuren) 1 2 3
  • 14. 3D-stehende Wellen (Chladni Figuren)
  • 15. 3D-stehende Wellen ("räumliche Chladni Figuren")
  • 16. 3D-stehende Wellen ("räumliche Chladni Figuren")
  • 17. listenweise and punktweise Trace- Methode (HSV Färbung)
  • 18. listenweise and punktweise Trace- Methode (HSV Färbung)
  • 19. spacial Chladni patterns

5.1.

Implicit surfaces as a network of implicit curves

– Roman Chijner

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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5.15.

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5.16.

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5.17.

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5.18.

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5.19.

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