## Wave |

In **wave** is a disturbance of a

The waves most commonly studied in physics are

Other types of waves include

Mechanical and electromagnetic waves may often seem to travel through space; but, while they can carry ^{[1]} ^{[2]} On the other hand, some waves do not appear to move at all, like

A physical wave is almost always confined to some finite region of space, called its **domain**. For example, the seismic waves generated by

A

- mathematical description
- wave in elastic medium
- sine waves
- plane waves
- standing waves
- physical properties
- mechanical waves
- electromagnetic waves
- quantum mechanical waves
- gravity waves
- gravitational waves
- see also
- references
- sources
- external links

A wave can be described just like a field, namely as a

The value of is a point of space, specifically in the region where the wave is defined. In mathematical terms, it is usually a

The value of can be any physical quantity of interest assigned to the point that may vary with time. For example, if represents the vibrations inside an elastic solid, the value of is usually a vector that gives the current displacement from of the material particles that would be at the point in the absence of vibration. For an electromagnetic wave, the value of can be the

For any dimension (1, 2, or 3), the wave's domain is then a

Sometimes one is interested in a single specific wave, like how the Earth vibrated after the

In some of those situations, one may describe such a family of waves by a function that depends on certain

For example, the sound pressure inside a

The parameter defines the amplitude of the wave (that is, the maximum sound pressure in the bore, which is related to the loudness of the note); is the speed of sound; is the length of the bore; and is a positive integer (1,2,3,...) that specifies the number of

As another example, it may be that the vibrations of a drum skin after a single strike depend only on the distance from the center of the skin to the strike point, and on the strength of the strike. Then the vibration for all possible strikes can be described by a function .

Sometimes the family of waves of interest has infinitely many parameters. For example, one may want to describe what happens to the temperature in a metal bar when it is initially heated at various temperatures at different points along its length, and then allowed to cool by itself in vacuum. In that case, instead of a scalar or vector, the parameter would have to be a function such that is the initial temperature at each point of the bar. Then the temperatures at later times can be expressed by a function that depends on the function (that is, a

Another way to describe and study a family of waves is to give a mathematical equation that, instead of explictly giving the value of , only constrains how those values can change with time. Then the family of waves in question consists of all functions that satisfy those constraints — that is, all

This approach is extremely important in physics, because the constraints usually are a consequence of the physical processes that cause the wave to evolve. For example, if is the temperature inside a block of some

where is the heat that is being generated per unit of volume and time in the neighborhood of at time (for example, by chemical reactions happening there); are the Cartesian coordinates of the point ; is the (first) derivative of with respect to ; and is the second derivative of relative to . (The simbol "" is meant to signify that, in the derivative with respect to some variable, all other variables must be considered fixed.)

This equation can be derived from the laws of physics that govern the

For another example, we can describe all possible sounds echoing within a container of gas by a function that gives the pressure at a point and time within that container. If the gas was initially at uniform temperature and composition, the evolution of is constrained by the formula

Here is some extra compression force that is being applied to the gas near by some external process, such as a

This same differential equation describes the behavior of mechanical vibrations and electromagnetic fields in a homogeneous isotropic non-conducting solid. Note that this equation differs from that of heat flow only in that the left-hand side is , the second derivative of with respect to time, rather than the first derivative . Yet this small change makes a huge difference on the set of solutions . This diferential equation is called "the"

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