Solving the Wave Equation with Separation of Variables and Guitar String Physics

Explore the fascinating world of wave equations and their applications in physics through this comprehensive 46-minute video lecture. Dive into the process of solving the Wave Equation using separation of variables, a fundamental technique in various fields of physics including optics and acoustics. Learn about initial conditions, boundary conditions, and the step-by-step process of separating variables to solve ordinary differential equations for space and time. Discover the general solution of the Wave Equation and its practical applications in guitar string physics. Gain insights into the Method of Characteristics as an alternative approach to solving wave equations. Perfect for students, educators, and enthusiasts looking to deepen their understanding of mathematical physics and its real-world applications.

Introduction .
Initial Conditions and Boundary Conditions for the Wave Equation.
Separation of Variables.
Solving the ODEs for Space and Time.
General Solution of the Wave Equation.
Recap.
Guitar String Physics.
Method of Characteristics.