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Longitudinal Wave Demonstration

Longitudinal Wave Demonstration
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2019-04-17 22:22
FunctionTrigonometryCalculusGraphing
This example demonstrates the propagation of a longitudinal wave (compression wave) by visualizing the displacement changes of the waveform. Key mathematical concepts involved include cosine and sine functions, definite integral, stochastic process, bar chart, functions, and logarithm. The construction leverages GeoGebra commands/objects like T, A, Displace, t, P0, dx, dt, P1-P32 to simulate wave displacement and propagation. It is suitable for high school and above students to learn wave theory, function graphs, and integral applications, as well as for physics teaching demonstrations.

GeoGebra Commands & Parameters

  1. Numeric T(5)
  2. Numeric A(2)
  3. Displace(x) = (A * sin((360° * x / T)))
  4. Numeric t(12.5)
  5. (Displace(t), 0)
  6. Numeric dx(0.5)
  7. Numeric dt(0.15)
  8. (dx + Displace(t - dt), 0)
  9. ((2 * dx) + Displace(t - (2 * dt)), 0)
  10. ((3 * dx) + Displace(t - (3 * dt)), 0)
  11. ((4 * dx) + Displace(t - (4 * dt)), 0)
  12. ((5 * dx) + Displace(t - (5 * dt)), 0)
  13. ((6 * dx) + Displace(t - (6 * dt)), 0)
  14. ((7 * dx) + Displace(t - (7 * dt)), 0)
  15. Numeric a(2)
  16. ((9 * dx) + Displace(t - (9 * dt)), 0)
  17. ((8 * dx) + Displace(t - (8 * dt)), 0)
  18. ((10 * dx) + Displace(t - (10 * dt)), 0)
  19. ((11 * dx) + Displace(t - (11 * dt)), 0)
  20. ((12 * dx) + Displace(t - (12 * dt)), 0)
  21. ((13 * dx) + Displace(t - (13 * dt)), 0)
  22. ((14 * dx) + Displace(t - (14 * dt)), 0)
  23. ((15 * dx) + Displace(t - (15 * dt)), 0)
  24. ((16 * dx) + Displace(t - (16 * dt)), 0)
  25. ((17 * dx) + Displace(t - (17 * dt)), 0)
  26. ((18 * dx) + Displace(t - (18 * dt)), 0)
  27. ((19 * dx) + Displace(t - (19 * dt)), 0)
  28. ((20 * dx) + Displace(t - (20 * dt)), 0)
  29. ((21 * dx) + Displace(t - (21 * dt)), 0)
  30. ((22 * dx) + Displace(t - (22 * dt)), 0)
  31. ((23 * dx) + Displace(t - (23 * dt)), 0)
  32. ((24 * dx) + Displace(t - (24 * dt)), 0)
  33. ((25 * dx) + Displace(t - (25 * dt)), 0)
  34. ((26 * dx) + Displace(t - (26 * dt)), 0)
  35. ((27 * dx) + Displace(t - (27 * dt)), 0)
  36. ((28 * dx) + Displace(t - (28 * dt)), 0)
  37. ((29 * dx) + Displace(t - (29 * dt)), 0)
  38. ((30 * dx) + Displace(t - (30 * dt)), 0)
  39. ((31 * dx) + Displace(t - (31 * dt)), 0)
  40. ((32 * dx) + Displace(t - (32 * dt)), 0)
  41. ((-dx) + Displace(t + dt), 0)
  42. (((-2) * dx) + Displace(t + (2 * dt)), 0)
  43. (((-3) * dx) + Displace(t + (3 * dt)), 0)
  44. (((-4) * dx) + Displace(t + (4 * dt)), 0)
  45. (((-5) * dx) + Displace(t + (5 * dt)), 0)
  46. (((-6) * dx) + Displace(t + (6 * dt)), 0)
  47. (((-7) * dx) + Displace(t + (7 * dt)), 0)
  48. Boolean ShowAll(true)