Space Elevator Tether Wave Propagation

This is a 2D companion to the 3D Space Elevator Tether Taper Profile simulator, built around a genuinely different piece of physics from the same tether. Instead of evaluating the closed-form taper equation and rendering the resulting static shape, this simulator numerically integrates the transverse wave equation along the tether with a finite-difference solver, so what you see is a live time-domain simulation of a plucked string — except the "string" runs from Earth's surface to a counterweight beyond geostationary orbit. The payoff is a clean, testable physics result: because the taper is designed to hold constant tensile stress at every altitude, the tether's cross-sectional area cancels out of the wave-speed formula entirely, so the transverse wave travels at the same speed everywhere along the cable no matter how much its thickness changes. Pick a material, pluck the tether, and watch the pulse cross tens of thousands of kilometres at a single, constant, material-set speed before reflecting off the fixed ground anchor and the free-swinging counterweight.