Wave
A propagating dynamic disturbance moves through one or more quantities, changing them from their equilibrium state. Periodic waves oscillate repeatedly about a resting value at some frequency. When the entire waveform travels in one direction, it is called a travelling wave. A pair of superimposed periodic waves traveling in opposite directions creates a standing wave. In a standing wave, the amplitude of vibration has nulls at positions where the wave amplitude appears smaller or even zero. These disturbances transfer energy without transferring particles in the medium. Viewed microscopically, waves are changes in physical property values resulting from delayed responses to adjacent regions. Properties like pressure, temperature, height, or gravitational force can exhibit these behaviors. Rotation of an electric dipole produces electromagnetic waves that propagate at the speed of light. Mutual rotation of binary stars generates gravitational waves with similar propagation speeds.
In mechanical waves, stress and strain fields oscillate about a mechanical equilibrium within a physical medium. Sound waves are variations of local pressure and particle motion that propagate through air or water. Seismic waves travel through Earth's layers as body waves or surface waves. Gravity waves form in fluid media when gravity or buoyancy works to restore equilibrium. Surface waves on water combine transverse and longitudinal motions so points follow orbital paths. Electromagnetic waves involve coupling between electric and magnetic fields according to Maxwell's equations. James Clerk Maxwell showed in the 19th century that electric and magnetic fields satisfy the wave equation in vacuum. Hertz experimentally confirmed this unification of light and electromagnetic waves by the end of the 1880s. Electromagnetic waves include radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. These waves can travel through vacuum and some dielectric media where they remain transparent.
A wave is described mathematically by a function mapping space and time onto a field value. For scalar fields the value is a number while vector fields yield vectors. Tensor fields produce tensor values at each point. The wave domain is a subset of space where the function value is defined for any point. When studying vibrations inside an elastic solid, the value represents current displacement from material particles. In fluid dynamics, velocity vectors describe motion at specific points. Chemical reactions use concentration as the variable quantity within reaction medium neighborhoods. Partial differential equations constrain how these values change with time rather than explicitly giving them. The heat equation describes temperature evolution in homogeneous isotropic solid materials. It involves derivatives with respect to spatial coordinates and time. The wave equation differs from heat flow only in having second time derivatives instead of first derivatives. This small change creates huge differences in solution sets. General solutions rely on Duhamel's principle for linear systems. D'Alembert's formula represents component waveforms traveling through media in opposite directions.
When a wave strikes a reflective surface it changes direction so incident angles equal reflected angles relative to normal lines. Refraction occurs when waves pass from one medium into another changing their speed. Snell's law relates incidence and refraction directions to refractive indices of two materials. Diffraction effects become pronounced when obstacle sizes match wavelengths of the wave. Interference patterns form when waves cross in regions where field quantities add according to superposition principles. If waves share frequency and fixed phase relationships, positions exist where amplitudes add or cancel completely. Polarization arises when transverse wave motion occurs simultaneously in orthogonal directions. Linear polarization oscillates in only one plane perpendicular to travel direction. Electromagnetic waves propagating in free space can be polarized using filters. Dispersion happens when phase velocity depends on wave frequency as seen when white light passes through prisms. Isaac Newton recognized that this meant white light contained mixtures of different colors. The Doppler effect describes frequency changes relative to observers moving near sources. Christian Doppler described this phenomenon in 1842 while working with Austrian physics concepts.
Standing waves arise when boundaries block further propagation causing reflection back toward sources. Nodes appear at bridge and nut positions where opposed waves are antiphase and cancel each other. Antinodes occur halfway between nodes where counter-propagating waves enhance each other maximally. No net energy propagates over time within standing wave systems. Solitons maintain their shape while propagating at constant velocities through media. These self-reinforcing packets result from cancellations of nonlinear and dispersive effects in the medium. Dispersive properties mean wave speed depends on frequency within certain systems. Shock waves form when disturbances move faster than local sound speeds in fluids. They carry abrupt nearly discontinuous changes in pressure temperature and density. Gravitational waves represent disturbances in spacetime curvature predicted by Einstein's general relativity theory. First observations of gravitational waves were announced on the 11th of February 2016 after decades of searching. Body waves travel through Earth interiors along paths controlled by material density and stiffness variations. Primary and secondary seismic waves produce different particle motions resulting in distinct behaviors. Surface waves like Rayleigh waves and Love waves travel differently through solid materials.
The Schrödinger equation describes wave-like behavior of particles in quantum mechanics contexts. Solutions to this equation are wave functions describing probability densities of particles. Louis de Broglie postulated that all particles with momentum possess wavelengths defined by Planck constants. Electrons in CRT displays have de Broglie wavelengths around 10^-13 meters. A wave function representing such particles traveling in k-directions uses specific mathematical forms. Gaussian wave packets localize particles by superposing different wavelengths ranging around central values. The Fourier transform of a Gaussian remains itself as a Gaussian shape. Narrow wavelength ranges necessary for localization create larger spreads in required wavelengths. Heisenberg uncertainty principle governs these relationships between spatial extent and wave vector spread. Dirac equations detail electromagnetic interactions while accounting for fine hydrogen spectrum details experimentally confirmed later. These equations implied existence of antimatter previously unsuspected and unobserved until experimental verification occurred. Quantum field theory reinterprets Dirac equations to describe spin-1/2 particles corresponding to quantum fields.
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Common questions
What is a wave in physics?
A propagating dynamic disturbance moves through one or more quantities, changing them from their equilibrium state. Periodic waves oscillate repeatedly about a resting value at some frequency.
When were gravitational waves first observed?
First observations of gravitational waves were announced on the 11th of February 2016 after decades of searching. These disturbances represent changes in spacetime curvature predicted by Einstein's general relativity theory.
How do electromagnetic waves propagate according to Maxwell's equations?
Rotation of an electric dipole produces electromagnetic waves that propagate at the speed of light. James Clerk Maxwell showed in the 19th century that electric and magnetic fields satisfy the wave equation in vacuum.
Who described the Doppler effect and when did this occur?
Christian Doppler described this phenomenon in 1842 while working with Austrian physics concepts. The Doppler effect describes frequency changes relative to observers moving near sources.
What are standing waves and how do they form?
Standing waves arise when boundaries block further propagation causing reflection back toward sources. Nodes appear at bridge and nut positions where opposed waves are antiphase and cancel each other.