Longitudinal stress waves in elastic rods obey ∂²u/∂t² = c² ∂²u/∂x², where c = √(E/ρ) is the wave speed (E = Young's modulus, ρ = density). At a free end, waves reflect with the same sign (displacement); at a fixed end, they invert. This is the basis for Split-Hopkinson (Kolsky) bar experiments used to measure dynamic material properties at high strain rates.