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Wave Pulse Addition Practice

Wave Pulse Addition Practice
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2018-03-28 20:29
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the graphical representation of adding two wave pulses, illustrating key mathematical concepts such as wave superposition, similar triangles, trigonometric functions, plane geometry, scatter plots, and arithmetic operations. It is constructed using GeoGebra commands like Segment, Ray, Polygon, Point, and Intersect, making it suitable for high school students studying wave theory, geometric constructions, and function graphing.

GeoGebra Commands & Parameters

  1. Segment(L1, A5) → f
  2. Segment(A5, B5) → g
  3. Segment(B5, C5) → h
  4. Segment(C5, D5) → i
  5. Segment(D5, E5) → j
  6. Segment(E5, R1) → k
  7. Segment(L2, E6) → l
  8. Segment(E6, D6) → m
  9. Segment(D6, C6) → n
  10. Segment(C6, B6) → p
  11. Segment(B6, A6) → q
  12. Segment(A6, R2) → r
  13. Ray(L1, A) → q_1
  14. Ray(L2, B) → r_1
  15. Segment(R2, L1) → a_1
  16. Segment(R1, L2) → b_1
  17. Segment(I1, A7) → c_1
  18. Segment(A7, B7) → d_1
  19. Segment(B7, C7) → e_1
  20. Segment(C7, D7) → f_2
  21. Segment(E7, H1) → h_2
  22. Segment(E8, D8) → i_2
  23. Segment(D8, C8) → j_2
  24. Segment(C8, B8) → k_2
  25. Segment(B8, A8) → l_2
  26. Segment(A8, H2) → m_2
  27. Segment(I2, E8) → n_2
  28. Segment(B25, B27) → p_2
  29. Segment(B27, D8) → q_2
  30. Segment(C24, C26) → r_2
  31. Segment(C26, C28) → s_2
  32. Segment(C28, C8) → t_2
  33. Segment(D23, D25) → a_2
  34. Segment(D25, D27) → b_2
  35. Segment(D27, D29) → c_2
  36. Segment(D29, B8) → d_2
  37. Segment(E22, E24) → e_2
  38. Segment(E24, E26) → f_3
  39. Segment(E30, A8) → i_3
  40. Segment(E26, E28) → g_3
  41. Segment(E28, E30) → h_3
  42. Segment(D7, B25) → j_3
  43. Segment(C24, C7) → k_3
  44. Segment(D23, B7) → l_3
  45. Segment(E22, A7) → m_3
  46. Segment(F23, F25) → q_3
  47. Segment(F25, F27) → r_3
  48. Segment(F27, F29) → s_3
  49. Segment(G24, G26) → b_3
  50. Segment(C8, G24) → c_3
  51. Segment(G26, G28) → d_3
  52. Segment(B8, H25) → g_4
  53. Segment(H25, H27) → h_4
  54. Ray(I1, E) → k_4
  55. Segment(H1, I2) → l_4
  56. Ray(I2, E) → p_4
  57. Segment(H2, I1) → q_4
  58. Segment(G28, C7) → e_3
  59. Segment(F29, D7) → t_3
  60. Segment(H27, B7) → t
  61. Segment(E8, D8) → s
  62. Segment(D8, F23) → b
  63. Segment(A8, A7) → c
  64. Segment(I1, E22) → d
  65. Segment(E30, H2) → e
  66. Segment(R2, D) → t_1
  67. Segment(H2, F) → m_4
  68. Segment(R1, C) → s_1
  69. Segment(H1, F) → n_4
  70. Polygon(H, I, J, K) → q1, h_1, i_1, j_1, k_1
  71. Segment(L, M) → f_1
  72. Segment(M, N) → g_1
  73. Segment(N, O) → l_1
  74. Segment(O, P) → m_1
  75. Segment(P, O) → n_1
  76. Segment(O, P) → p_1
  77. Segment(Q, R) → n_3
  78. Segment(R, S) → p_3
  79. Segment(S, T) → a_3
  80. Segment(T, U) → f_4
  81. Segment(V, W) → i_4
  82. Segment(W, Z) → j_4
  83. Segment(Z, A_1) → r_4
  84. Segment(A_1, B_1) → s_4
  85. Segment(B_1, C_1) → t_4
  86. Segment(D_1, E_1) → a_4
  87. Segment(E_1, F_1) → b_4
  88. Segment(F_1, G_1) → c_4
  89. Segment(G_1, H_1) → d_4
  90. Segment(H_1, I_1) → e_4
  91. Segment(I_1, J_1) → f_5
  92. Segment(K_1, L_1) → g_5
  93. Segment(L_1, M_1) → h_5
  94. Segment(M_1, N_1) → i_5
  95. Segment(N_1, O_1) → j_5
  96. Segment(P_1, Q_1) → k_5
  97. Segment(Q_1, R_1) → l_5
  98. Segment(R_1, S_1) → m_5
  99. Segment(S_1, T_1) → n_5
  100. Segment(T_1, U_1) → p_5
  101. Segment(U_1, V_1) → q_5
  102. Segment(G, W_1) → r_5
  103. Segment(Z_1, W_1) → s_5
  104. Segment(Z_1, A_2) → t_5
  105. Segment(A_2, B_2) → a_5
  106. Segment(C_2, D_2) → b_5
  107. Segment(D_2, E_2) → c_5
  108. Segment(E_2, F_2) → d_5
  109. Segment(F_2, G_2) → e_5
  110. Segment(H_2, I_2) → f_6
  111. Segment(I_2, J_2) → g_6
  112. Segment(J_2, K_2) → h_6
  113. Segment(K_2, L_2) → i_6
  114. Segment(L_2, M_2) → j_6
  115. Segment(M_2, N_2) → k_6
  116. Segment(O_2, P_2) → l_6
  117. Segment(P_2, Q_2) → m_6
  118. Segment(Q_2, R_2) → n_6
  119. Segment(R_2, S_2) → p_6
  120. Segment(T_2, U_2) → q_6
  121. Segment(U_2, V_2) → r_6
  122. Segment(V_2, W_2) → s_6
  123. Segment(W_2, Z_2) → t_6
  124. Segment(A_3, B_3) → a_6
  125. Segment(B_3, C_3) → b_6
  126. Segment(C_3, D_3) → c_6
  127. Segment(D_3, E_3) → d_6
  128. Segment(E_3, F_3) → e_6
  129. Segment(G_3, H_3) → f_7
  130. Segment(H_3, I_3) → g_7
  131. Segment(I_3, J_3) → h_7
  132. Segment(J_3, K_3) → i_7
  133. Segment(K_3, L_3) → j_7
  134. Segment(L_3, M_3) → k_7
  135. Segment(N_3, O_3) → l_7
  136. Segment(O_3, P_3) → m_7
  137. Segment(P_3, Q_3) → n_7
  138. Segment(Q_3, R_3) → p_7
  139. Segment(S_3, T_3) → q_7
  140. Segment(T_3, U_3) → r_7
  141. Segment(U_3, V_3) → s_7
  142. Segment(V_3, W_3) → t_7
  143. Segment(W_3, Z_3) → a_7
  144. Segment(A_4, B_4) → b_7
  145. Segment(B_4, C_4) → c_7
  146. Segment(C_4, D_4) → d_7
  147. Segment(D_4, E_4) → e_7
  148. Segment(F_4, G_4) → f_8
  149. Segment(G_4, H_4) → g_8
  150. Segment(H_4, I_4) → h_8
  151. Segment(I_4, J_4) → i_8
  152. Segment(K_4, L_4) → j_8
  153. Segment(L_4, M_4) → k_8
  154. Segment(M_4, N_4) → l_8
  155. Segment(N_4, O_4) → m_8
  156. Segment(O_4, P_4) → n_8
  157. Segment(P_4, Q_4) → p_8
  158. Segment(Q_4, P_4) → q_8
  159. Point(k_1) → R_4
  160. Point(i_1) → S_4
  161. Segment(R_4, S_4) → r_8
  162. Intersect(k_1, xAxis) → T_4
  163. Intersect(i_1, xAxis) → U_4
  164. Segment(T_4, U_4) → s_8
  165. Segment(D7, E7) → g_2
  166. Ray(Z_4, A_5) → t_8
  167. Segment(E7, E8) → a_8
  168. Segment((B32, -6), (B32, -22)) → B33
  169. Segment((C32, -6), (C32, -22)) → C33
  170. Segment((D32, -6), (D32, -22)) → D33
  171. Segment((E32, -6), (E32, -22)) → E33
  172. Segment((F32, -6), (F32, -22)) → F33
  173. Segment((G32, -6), (G32, -22)) → G33
  174. Segment((H32, -6), (H32, -22)) → H33
  175. Segment((I32, -6), (I32, -22)) → I33
  176. Segment((J32, -6), (J32, -22)) → J33
  177. Segment((K32, -6), (K32, -22)) → K33
  178. Segment((L32, -6), (L32, -22)) → L33
  179. Segment((M32, -6), (M32, -22)) → M33
  180. Segment((N32, -6), (N32, -22)) → N33
  181. Segment((O32, -6), (O32, -22)) → O33
  182. Segment((P32, -6), (P32, -22)) → P33
  183. Segment(AAA2, AAA3) → b_8
  184. Segment(AAA4, AAA3) → c_8
  185. Segment(AAA4, AAA5) → d_8
  186. Segment(AAA5, AAA6) → e_8
  187. Segment(AAA6, AAA7) → f_9
  188. Segment(AAA7, AAA8) → g_9
  189. Segment(AAA8, AAA9) → h_9
  190. Segment(AAA10, AAA9) → p_9
  191. Segment(AAA2, AAA1) → q_9
  192. Segment(AAA11, AAA10) → i_9