Wave Equation: d'Alembert's Formula Interactive Demo

① This GeoGebra example interactively demonstrates d'Alembert's formula for the one-dimensional wave equation, showing how initial displacement and velocity profiles evolve into left- and right-traveling waves that superpose. ② Core mathematical concepts include the wave equation (a partial differential equation), d'Alembert's solution, traveling wave decomposition, initial conditions, superposition principle, and the use of integration to compute the solution. ③ Construction highlights: from the summary, the applet uses commands such as Textfield, Integral, and If, along with multiple buttons (button1-4) and sliders (speed, max, time) to control parameters. Objects include f0 and g0 (initial condition functions), f, intg (integral result), u (solution function), wave (wave plot), and input boxes InputBox1-4 for interactive modification of functions and parameters. ④ Suitable for university-level courses on partial differential equations or mathematical physics, as well as advanced high school physics, to visualize the physical meaning of d'Alembert's formula and wave propagation.