Wave Equation: Mechanical Systems

This lecture covers the wave equation for mechanical systems, including the different velocities of waves on strings. It introduces the d'Alembert wave equation, a second-order linear partial differential equation describing waves. The presentation includes simulations on waves, illustrations of physical waves, and examples of disturbances following the wave equation. The lecture also discusses solutions to the wave equation, phase velocity, and examples of waves following d'Alembert. It concludes with a summary of the generalized wave equation adapted to a string, emphasizing the importance of the phase velocity in wave propagation.