A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are oscillations around almost fixed locations.

Definitions

Agreeing on a single, all-encompassing definition for the term wave is non-trivial. A vibration can be defined as a back-and-forth motion around a point m around a reference value. However, defining the necessary and sufficient characteristics that qualify a phenomenon to be called a wave is, at least, flexible. The term is often understood intuitively as the transport of disturbances in space, not associated with motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium (Hall, 1980: 8). However, this notion is problematic for a standing wave (for example, a wave on a string), where energy is moving in both directions equally, or for electromagnetic / light waves in a vacuum, where the concept of medium does not apply.

For such reasons, wave theory represents a peculiar branch of physics that is concerned with the properties of wave processes independently from their physical origin (Ostrovsky and Potapov, 1999). The peculiarity lies in the fact that this independence from physical origin is accompanied by a heavy reliance on origin when describing any specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a mechanical rather than an electromagnetic wave-like transfer / transformation of vibratory energy. Concepts such as mass, momentum, inertia, or elasticity, become therefore crucial in describing acoustic (as opposed to optic) wave processes. This difference in origin introduces certain wave characteristics particular to the properties of the medium involved (for example, in the case of air: vortices, radiation pressure, shock waves, etc., in the case of solids: Rayleigh waves, dispersion, etc., and so on).

Other properties, however, although they are usually described in an origin-specific manner, may be generalized to all waves. For example, based on the mechanical origin of acoustic waves there can be a moving disturbance in space-time if and only if the medium involved is neither infinitely stiff nor infinitely pliable. If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion (or rather infinitely fast wave motion). On the other hand, if all the parts were independent, then there would not be any transmission of the vibration and again, no wave motion (or rather infinitely slow wave motion). Although the above statements are meaningless in the case of waves that do not require a medium, they reveal a characteristic that is relevant to all waves regardless of origin: within a wave, the phase of a vibration (that is, its position within the vibration cycle) is different for adjacent points in space because the vibration reaches these points at different times.