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Sine Wave Addition by Apolinario "Sam" Ortega

Sine Wave Addition by Apolinario "Sam" Ortega
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2016-07-09 14:58
FunctionTrigonometryCalculusGraphing
This example demonstrates the phenomenon of superposition of two or more sine waves to form a composite wave pattern. Core mathematical concepts include sine functions, wave superposition principles, and analytical geometry. Construction highlights involve commands/objects like Line, Point, Vector, OrthogonalLine, Mirror, Function, Intersect, and Segment from GeoGebra. Suitable for high school and above students learning function graph transformations, wave superposition, and for calculus teaching on derivatives and integrals applications.

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, 8.986839107117935)) → H
  21. Intersect(q, e, (12.566400000000001, 2.338236787157129)) → I
  22. Intersect(r, e, (12.566400000000001, -3.066924105724937)) → 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