wave

A wave is a disturbance that transfers energy through a medium or through space, without a net transport of matter. Waves fall into two broad classes: mechanical waves, which require a medium such as air, water, or rock to propagate; and electromagnetic waves, which can travel through vacuum as well as through matter. Examples include sound waves, water surface waves, seismic waves, and electromagnetic waves such as radio, microwaves, visible light, and X-rays.

Key properties describe a wave's behavior. The wavelength (lambda) is the distance between repeating points, the frequency (f) is how many cycles pass a given point per second, and the speed (v) is v = f lambda for a simple carrier. Amplitude measures the maximum disturbance. Mechanical waves transfer energy and momentum through a medium, while electromagnetic waves can propagate without a medium. In many cases, particles oscillate locally while the wave energy moves through the medium.

Waves obey the superposition principle: when two or more waves meet, their disturbances add together. This leads to constructive or destructive interference and can form standing waves under certain boundary conditions. Other important effects include reflection at boundaries, refraction when crossing interfaces, diffraction around obstacles, and dispersion when wave speed depends on frequency. Polarization describes the orientation of transverse waves.

Applications span science and engineering. Acoustic waves enable hearing and medical imaging; seismic waves probe Earth's interior; surface and ocean waves influence coastal processes. Electromagnetic waves underpin communications, radar, sensing, and a wide range of imaging technologies. The mathematics of waves is often expressed through the wave equation, with Maxwell’s equations providing the foundation for electromagnetic waves.