# A report on Wave equation

Second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves).

- Wave equation14 related topics with Alpha

## Wave

2 linksPropagating dynamic disturbance of one or more quantities.

Propagating dynamic disturbance of one or more quantities.

Waves are often described by a wave equation (standing wave field of two opposite waves) or a one-way wave equation for single wave propagation in a defined direction.

## Partial differential equation

1 linksEquation which imposes relations between the various partial derivatives of a multivariable function.

Equation which imposes relations between the various partial derivatives of a multivariable function.

The theory of elliptic, parabolic, and hyperbolic equations have been studied for centuries, largely centered around or based upon the standard examples of the Laplace equation, the heat equation, and the wave equation.

## Boundary value problem

1 linksDifferential equation together with a set of additional constraints, called the boundary conditions.

Differential equation together with a set of additional constraints, called the boundary conditions.

Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

## Standing wave

1 linksWave that oscillates in time but whose peak amplitude profile does not move in space.

Wave that oscillates in time but whose peak amplitude profile does not move in space.

Equivalently, this boundary condition of the "free end" can be stated as ∂y/∂x = 0 at, which is in the form of the Sturm–Liouville formulation.

## Superposition principle

1 linksSum of the responses that would have been caused by each stimulus individually.

Sum of the responses that would have been caused by each stimulus individually.

In any system with waves, the waveform at a given time is a function of the sources (i.e., external forces, if any, that create or affect the wave) and initial conditions of the system.

## Separation of variables

1 linksAny of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

Any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

The method of separation of variables is also used to solve a wide range of linear partial differential equations with boundary and initial conditions, such as the heat equation, wave equation, Laplace equation, Helmholtz equation and biharmonic equation.

## Helmholtz equation

1 links[[Image:Helmholtz source.png|right|thumb|Two sources of radiation in the plane, given mathematically by a function

[[Image:Helmholtz source.png|right|thumb|Two sources of radiation in the plane, given mathematically by a function

The Helmholtz equation has a variety of applications in physics, including the wave equation and the diffusion equation, and it has uses in other sciences.

## Jean le Rond d'Alembert

0 linksFrench mathematician, mechanician, physicist, philosopher, and music theorist.

French mathematician, mechanician, physicist, philosopher, and music theorist.

D'Alembert's formula for obtaining solutions to the wave equation is named after him.

## Inhomogeneous electromagnetic wave equation

0 linksIn electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and currents.

## One-way wave equation

0 linksFirst-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity.

First-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity.

It contrasts with the second-order two-way wave equation describing a standing wavefield resulting from superposition of two waves in opposite directions.