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In mathematics and science, a wave is a periodic disturbance in space and time, possibly transferring energy to or through a spacetime region. A wave equation describes how the disturbance proceeds over time. The form of this equation varies depending on the type of wave.

Waves can be classified in several ways, including

  • whether or not the wave produces a net propagation of energy over time, i.e.,
    • Standing waves remain confined to a given space in the wave's medium.
    • Traveling waves move through a space in a medium. The wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass transport. For example, a cork on rippling water will bob up and down, staying in about the same place while the wave itself moves onwards.
  • the medium in which the disturbance occurs, i.e.,
    • Mechanical waves, which propagate through matter. In each period of a mechanical wave, its medium is first deformed, then restoring forces reverse the deformation. For example, sound waves propagate when air molecules bump into their neighbors, transferring energy to them, causing a cascade of collisions in a given direction. But air molecules collide with their neighbors elastically, bouncing back in the opposite direction. That restoring force prevents molecules from continuing to travel in the direction of the wave.
    • Vacuum waves, e.g. electromagnetic radiation (including visible light, ultraviolet radiation, infrared radiation, gamma rays, X-rays, and radio waves), can travel through empty space. This type of wave consists of periodic oscillations in electrical and magnetic fields. Researchers believe that gravitational waves also travel through space, although gravitational waves have never been directly detected.
  • the direction of the wave disturbance relative to its direction of propagation, i.e.,
    • Transverse waves oscillate perpendicularly to the motion of the wave.
    • Longitudinal waves oscillate in the same direction as the wave.
  • the spatial dimensionality of the wave. Disturbances may occur in, e.g., one or two spatial dimensions.

One-dimensional standing waves; the fundamental mode and the first 6 overtones.

A two-dimensional standing wave on a disk; this is the fundamental mode.

A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.


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