Wave Equation: Mechanical System and Phase Velocities on Strings

This lecture covers the development and application of the wave equation for mechanical systems, explaining the different velocities of waves on strings and introducing the d'Alembert wave equation. It explores mechanical waves on strings under tension, solutions to the wave equation, consistency checks, and examples of waves following d'Alembert. The lecture also discusses the generalized wave equation, its adaptation to strings, and the adjustment of phase velocity formula. It concludes with the introduction of the polarization vector in the context of transverse waves.