Let's Learn Physics: Good Vibrations from Wave Equations

The wave equation is not only important due to the fact that it describes many different physical phenomena, but also because it naturally leads us to some very interesting mathematical results and techniques. In this stream, we will talk about methods we can use to solve the wave equation with various boundary conditions, including the method of images and Fourier series for different types of functions. We will see that the latter is very similar to decomposing vectors in 3-dimensional space into orthonormal basis vectors where the analog of the basis vectors is played by sets of basis functions which satisfy their own version of orthonormality. Finally, we will introduce the idea of a Fourier transform and duality in physics.