MathPlotAI Logo MathPlotAI

Wave Reflection at a Plane Boundary

Wave Reflection at a Plane Boundary
Loading the math board and drawing, please wait…
2016-01-10 08:29
AngleTrigonometryGeometric Construction
This example demonstrates the reflection of wave fronts off a barrier, showing how the angle of incidence varies. Key math concepts include reflection laws, angles, trigonometry, and slopes. The construction utilizes GeoGebra commands like Rotate, Line, Intersect, OrthogonalLine, Point, Ray, Angle, Polygon, Segment, and Sequence. It is suitable for high school physics and mathematics education to understand wave reflection properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Rotate(B, 90° - α, C) → B'
  2. Line(B', C) → c
  3. Intersect(y = 2, c) → N1
  4. Intersect(l, c) → P
  5. OrthogonalLine(P, c) → pPerp
  6. Point(pPerp) → K
  7. Point(pPerp) → L
  8. Rotate(K, (-α), P) → L'
  9. Ray(P, L') → m
  10. Angle(B, C, B') → β
  11. Intersect(c, yAxis) → A
  12. Point(yAxis) → G
  13. Intersect(c, b) → D
  14. Polygon(A, D, E, G) → poly1, a, d, e, g
  15. Point(yAxis) → F
  16. Point(b) → H
  17. Polygon(F, H, D, A) → poly2, f, h, d_1, a_1
  18. Segment(K, L) → norm
  19. Intersect(l, yAxis) → PA
  20. Segment(PA, P) → p1
  21. Angle(K, P, PA) → θ_i
  22. Intersect(z, m) → M
  23. Segment(P, M) → p2
  24. Angle(K, P, L') → θ_r
  25. Sequence(((w * (i + t)), 2), i, 0, 11) → list1
  26. Sequence(((w * (t + i)), 4), i, 0, 11) → list2
  27. Sequence(Segment[Element[list1, i], Element[list2, i]], i, 1, 12) → wi
  28. Intersect(y = 4, c) → N2
  29. Line(N1, p2) → j1
  30. Line(N2, p2) → j2
  31. OrthogonalLine(N1, j1) → lr1
  32. Intersect(j2, lr1) → N
  33. Sequence((r1x + ((w * dx) * (t + dt + i)), 2 + ((w * dy) * (t + dt + i))), i, -2, 10) → list3
  34. Sequence((rx + ((w * dx) * (t + dt + i)), ry + ((w * dy) * (t + dt + i))), i, -2, 10) → list4
  35. Sequence(Segment[Element[list3, i], Element[list4, i]], i, 1, 11) → wr