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2D Wave Demonstration

2D Wave Demonstration
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2017-10-09 07:06
VectorFunctionParametric EquationGeometric Construction
In collections surface 3D /3D-Oberflächen 1
This example demonstrates the propagation and variation of 2D waves in a plane. It involves core mathematical concepts such as function graphs, parametric equations, vector operations, and geometric transformations. Construction highlights include the use of GeoGebra commands Corner, CornerThreeD, Text, Textfield, Sequence, and objects like λ_1, A_{2D}, A_{3D}, f_1, s_1, time, ShiftS, tMax, o, G1Corner series, G2Corner series, G3DCorner series, G2Text series, and TabWaveA to dynamically visualize wave parameters and geometric relationships. Suitable for high school and above students and teachers in mathematics and physics for teaching demonstrations and explorations.

GeoGebra Commands & Parameters

  1. Corner(1, 1) → G1Corner_1
  2. Corner(1, 2) → G1Corner_2
  3. Corner(1, 3) → G1Corner_3
  4. Corner(1, 4) → G1Corner_4
  5. Corner(2, 3) → G2Corner_3
  6. Corner(2, 4) → G2Corner_4
  7. Corner(2, 2) → G2Corner_2
  8. Corner(2, 1) → G2Corner_1
  9. CornerThreeD(-1, 1) → G3DCorner_1
  10. CornerThreeD(-1, 2) → G3DCorner_2
  11. CornerThreeD(-1, 3) → G3DCorner_3
  12. CornerThreeD(-1, 4) → G3DCorner_4
  13. CornerThreeD(-1, 5) → G3DCorner_5
  14. CornerThreeD(-1, 6) → G3DCorner_6
  15. CornerThreeD(-1, 7) → G3DCorner_7
  16. CornerThreeD(-1, 8) → G3DCorner_8
  17. Text("(c) Oliver Fechtig") → G2TextCopyrightDummy
  18. Corner(G2TextCopyrightDummy, 1) → G2TextCopyrightCorner_1
  19. Corner(G2TextCopyrightDummy, 2) → G2TextCopyrightCorner_2
  20. Corner(G2TextCopyrightDummy, 3) → G2TextCopyrightCorner_3
  21. Corner(G2TextCopyrightDummy, 4) → G2TextCopyrightCorner_4
  22. Textfield(time) → G2TimeIndex
  23. Text(G2TextCopyrightDummy) → G2TextCopyright
  24. Sequence(Circle[A_{3D} + (0, 0, (2 * s_1)), (c * (time - (k * T_1) - T_1 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Minima_{A,3D}
  25. Sequence(Circle[A_{3D} + (0, 0, (2 * s_1)), (c * (time - (((2 * k) + 1) / 2 * T_1) - T_1 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Maxima_{A,3D}
  26. Sequence(Circle[A_{2D}, (c * (time - (((2 * k) + 1) / 2 * T_1) - T_1 / 4))], k, 0, 20) → Maxima_{A,2D}
  27. Sequence(Circle[A_{2D}, (c * (time - (k * T_1) - T_1 / 4))], k, 0, 20) → Minima_{A,2D}
  28. Sequence(Circle[B_{2D}, (c * (time - (((2 * k) + 1) / 2 * T_2) - T_2 / 4)), xOyPlane], k, 0, 20) → Maxima_{B,2D}
  29. Sequence(Circle[B_{2D}, (c * (time - (k * T_2) - T_2 / 4)), xOyPlane], k, 0, 20) → Minima_{B,2D}
  30. Sequence(Circle[B_{3D} + (0, 0, (2 * s_2)), (c * (time - (k * T_2) - T_2 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Minima_{B,3D}
  31. Sequence(Circle[B_{3D} + (0, 0, (2 * s_2)), (c * (time - (((2 * k) + 1) / 2 * T_2) - T_2 / 4)), Vector[(0, 0, 1)]], k, 0, 20) → Maxima_{B,3D}