Wave Evolution on a String
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This example demonstrates the evolution of a wave on a string of length L (L=1) using the d'Alembert formula. It involves core mathematical concepts such as partial differential equations, definite integrals, function graphing, and geometric transformations. The construction leverages GeoGebra commands and objects like t, D, E, F, G, f, ω, χ, ξ, μ, κ, η, ζ, γ, β, s, r, q, λ, h, g, ν, ϕ, ψ, p, f_1. Suitable for high school and above students to understand numerical solutions and dynamic changes in wave equations.
GeoGebra Commands & Parameters
Numeric t(0.25)D(x) = x - floor(x)E(x) = (2 * D(x / 2))F(x) = E(x + t)G(x) = E(x - t)f(x) = If[0 ≤ F(x) ≤ 1 / 4, 0, 0]ω(x) = If[1 / 4 + 1 ≤ F(x) ≤ 1 / 2 + 1, (-4 * (F(x) - 2 + 3 / 4)), 0]χ(x) = If[1 / 4 + 1 ≤ G(x) ≤ 1 / 2 + 1, (-4 * (G(x) - 2 + 3 / 4)), 0]ξ(x) = If[1 ≤ G(x) ≤ 1 + 1 / 4, 0, 0]μ(x) = If[1 / 2 ≤ F(x) ≤ 3 / 4, (4 * (3 / 4 - F(x))), 0]κ(x) = If[1 / 2 + 1 ≤ G(x) ≤ 3 / 4 + 1, (4 * (1 / 4 - 2 + G(x))), 0]η(x) = If[1 ≤ F(x) ≤ 1 + 1 / 4, 0, 0]ζ(x) = If[3 / 4 + 1 ≤ G(x) ≤ 2, 0, 0]γ(x) = If[0 ≤ G(x) ≤ 0.25, 0, 0]β(x) = If[3 / 4 + 1 ≤ F(x) ≤ 2, 0, 0]s(x) = If[3 / 4 ≤ F(x) ≤ 1, 0, 0]r(x) = If[3 / 4 ≤ G(x) ≤ 1, 0, 0]q(x) = If[1 / 2 ≤ F(x) ≤ 3 / 4, (4 * (3 / 4 - F(x))), 0]λ(x) = If[1 / 2 + 1 ≤ F(x) ≤ 3 / 4 + 1, (4 * (1 / 4 - 2 + F(x))), 0]h(x) = If[1 / 2 ≤ G(x) ≤ 3 / 4, (4 * (3 / 4 - G(x))), 0]g(x) = If[1 / 4 ≤ G(x) ≤ 1 / 2, (4 * (G(x) - 1 / 4)), 0]ν(x) = If[1 / 4 ≤ F(x) ≤ 1 / 2, (4 * (F(x) - 1 / 4)), 0]ϕ(x) = r(x) + g(x) + h(x) + χ(x) + ξ(x) + κ(x) + ζ(x) + γ(x)ψ(x) = μ(x) + ν(x) + β(x) + ω(x) + η(x) + f(x) + s(x) + λ(x)p(x) = (1 / 2 * (ϕ(x) + ψ(x)))f_1(x) = If[0 ≤ x ≤ 1, p(x)]