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Adding 3rd Harmonic to Fundamental Frequency

Adding 3rd Harmonic to Fundamental Frequency
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2016-07-10 04:34
FunctionTrigonometryCoordinate Geometry
This example visualizes the waveform formed by adding a 3rd harmonic to the fundamental frequency. Key mathematical concepts include trigonometric functions and frequency addition. Using GeoGebra commands such as Line, Point, Vector, and Function, the waveform changes are demonstrated. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Point(a) → E
  3. Point(a) → D
  4. Vector(D, E) → u
  5. OrthogonalLine(A, u) → c
  6. Point(c) → B
  7. Point(c) → C
  8. Vector((x(D), y(B)), (x(E), y(B))) → v
  9. Vector((x(B), y(B) - 1), (x(B), y(B) + 1)) → b
  10. Point(c) → F
  11. Mirror(F, a) → F'
  12. Vector(F', F) → d
  13. Vector((x(D), y(C)), (x(E), y(C))) → w
  14. Vector((x(C), y(C) - 1), (x(C), y(C) + 1)) → z
  15. Point(a) → G
  16. Function(f, x(C) - 1, x(G)) → p
  17. Function(g, x(B) - 1, x(G)) → q
  18. Function(h, x(A) - 1, x(G)) → r
  19. OrthogonalLine(G, u) → e
  20. Intersect(p, e, (12.566400000000001, 8.998960332696414)) → H
  21. Intersect(q, e, (12.566400000000001, 2.4543534220062475)) → I
  22. Intersect(r, e, (12.566400000000001, -2.938686245297339)) → J
  23. Segment(H, G) → i
  24. Segment(H, J) → j
  25. Segment(J, G) → k
  26. Function(f, x(C) - 1, x(E)) → s
  27. Function(g, x(B) - 1, x(E)) → f_1
  28. Function(h, x(A) - 1, x(E)) → g_1

AI Drawing Prompt Reference

Draw a horizontal baseline with several points on it. From one point on the baseline, construct a perpendicular line and place two points on it, creating vectors with baseline points. Use these vectors to draw parallel lines, forming a grid. Take another point on the baseline, draw a perpendicular, and intersect it with three sine curves of different frequencies, yielding three intersection points. Connect these points to the baseline point to form a triangle. Finally, truncate the three curves to the interval between the baseline point and the perpendicular foot, showing the waveform formed by adding the 3rd harmonic to the fundamental frequency.
The prompt above was compiled from the original drawing commands and is for reference only.