The wave equation is a hyperbolic partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves …

Nov 16, 2022 · In this section we do a partial derivation of the wave equation which can be used to find the one dimensional displacement of a vibrating string. In addition, we also give the two …

In most cases, one can start from basic physical principles and from these derive partial differential equations (PDEs) that govern the waves. In Section 4.2 we will do this for …

Feb 24, 2025 · This page explores the physics and mathematics behind a tensioned guitar string, specifically focusing on one-dimensional wave equations governing vibrations. It discusses …

The wave equation models the propagation of waves, such as sound waves, light waves, or water waves, through a medium. It captures how these waves travel and change over time and space.

In these notes, we give the general solution to the wave equation. The wave equation is one of the rare PDEs that we can solve analytically with complete generality.

The wave equation is a linear second-order partial differential equation which describes the propagation of oscillations at a fixed speed in some quantity ...

es. These two equations will be called ”forced” and ”damped” respectively. In the ”forced” case, the wave equation is: utt c2uxx + h(x, t), where an example of the acting force is the gravitatio …

Dec 22, 2025 · The wave equation is the important partial differential equation del ^2psi=1/ (v^2) (partial^2psi)/ (partialt^2) (1) that describes propagation of waves with speed v. The form …

The wave equation is second order with respect to time t therefore we need two initial conditions to specifiy a unique solution. The initial conditions are functions f (x) and g (x) which determine …