Wave Equation on a Half Line

This GeoGebra example dynamically simulates the propagation of the wave equation on a half-line (x ≥ 0), visually demonstrating wave reflection at the boundary and superposition of left- and right-moving waves. Core mathematical concepts include partial differential equations, the one-dimensional wave equation, traveling wave solutions, boundary conditions (fixed or free end), and d'Alembert's formula. Construction highlights: sliders (a, t, speed) control time and wave speed; function objects (Functions, f0, f, g0, g) define initial displacement and velocity; the Integral command computes the integral term in d'Alembert's solution; Segment draws boundary or reference lines; objects u1 and u2 represent the two wave components, while b1 and b2 handle boundary interactions; a button (button1) resets or plays the animation; SelectedIndex and Element allow switching among multiple initial condition sets. This resource is ideal for university-level mathematical physics courses or advanced high school physics, helping learners grasp wave propagation, reflection, and solving initial-boundary value problems on semi-infinite domains.