waves

Waves are disturbances that propagate energy through space or a medium, often without a net transport of matter. They can be classified as mechanical waves, which require a surrounding medium (such as air, water, or rock), and electromagnetic waves, which can travel through vacuum as well as media (for example light, radio waves).

Common wave parameters include wavelength λ, frequency f (or period T), amplitude A, and propagation speed v. The relation v = fλ ties these together for a given wave. The speed depends on the type of wave and the medium; for light, speed in a medium equals c divided by the refractive index, while in vacuum light travels at c in all directions. Mechanical waves move more slowly, governed by the medium’s elasticity and inertia.

Waves can be transverse, with particle motion perpendicular to the direction of travel, or longitudinal, with motion parallel to it; many real waves, such as on a string or water surfaces, show a combination. Waves may also exhibit dispersion, where speed varies with frequency, and they can propagate along interfaces as surface waves.

Interactions with boundaries produce reflection and refraction; interference from superposition creates constructive or destructive patterns; diffraction spreads waves around obstacles. These phenomena, together with the principle of superposition, underpin much of acoustics, optics, and communications.

Examples include water waves, sound waves, seismic waves, and electromagnetic waves such as visible light, radio, and X-ray. The wave concept has a long history in science, from Huygens’ wave theory of light to modern quantum descriptions that treat energy as quantized packets accompanying waves.