Waves:

A wave is a dynamic disturbance that propagates and causes a change in equilibrium of one or more parameters in physics, mathematics, and related subjects. Quantities may oscillate regularly around an equilibrium (resting) value at certain frequency if a wave is periodic. A traveling wave is one in which the entire waveform moves in one direction; in contrast, a standing wave is one in which two periodic waves are overlaid and move in the opposing directions. In a standing wave, there are some points where the wave amplitude seems reduced or even zero, and these positions have null vibration amplitudes. A wave equation (standing wave field comprising two opposing waves) or a one-way wave equation (for single wave propagation in a certain direction) is frequently used to describe waves.

 

In classical physics, two types of waves are most frequently examined. Stress and strain fields oscillate around a mechanical equilibrium in a mechanical wave. A mechanical wave is a local strain or deformation in a physical material that moves from particle to particle by generating local stresses that also generate strain in nearby particles. For instance, sound waves travel across a medium as fluctuations of the local pressure and particle motion.

 

Waves

Seismic waves, gravity waves, surface waves, string vibrations, and vortices are other examples of mechanical waves. According to Maxwell's equations, the electric and magnetic fields in an electromagnetic wave (like light) are coupled together to support wave propagation. A vacuum and some dielectric materials can both allow for the passage of electromagnetic waves (at wavelengths where they are considered transparent). Radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays, and gamma rays are some of the more precise names given to electromagnetic waves based on their frequencies (or wavelengths).

 

Other types of waves include reaction-diffusion waves, such as those produced by the Belousov-Zhabotinsky reaction, heat diffusion waves, plasma waves that combine mechanical deformations and electromagnetic fields, and many more. Gravitational waves are disturbances in spacetime that propagate in accordance with general relativity. Physical particles in the medium are not transferred by mechanical or electromagnetic waves, but they do transport energy, momentum, and information. Signals modeled as waves are explored in mathematics and electronics. On the other side, some waves, such standing waves and hydraulic jumps, have envelopes that are completely stationary. Some may be entirely static, such as the quantum mechanical probability waves.

 

Waves

A physical wave field is typically contained inside a domain, or limited area of space. For instance, the seismic waves produced by earthquakes are only important within and on the surface of the planet, therefore they can be disregarded from space. However, mathematical waves with infinite domains—which cover all of space—are frequently studied and are extremely helpful for comprehending physical waves with finite domains.

 

An important mathematics idealization is the plane wave, where the disturbance is the same along any (infinite) plane normal to a particular direction of motion. The simplest wave in mathematics is a sinusoidal plane wave in which the field exhibits simple harmonic motion at a single frequency at each point. Complex waves in linear media can typically be broken down into a number of sinusoidal plane waves with distinct propagation axes and/or frequencies.A plane wave is categorized as either a transverse wave or a longitudinal wave depending on whether the field disturbance at each site can be characterized by a vector perpendicular to the direction of propagation (also the direction of energy transfer). While electromagnetic plane waves are solely transverse and sound waves in fluids (such as air) can only be longitudinal, mechanical waves can be both transverse and longitudinal. The polarization of the wave, which can be a crucial characteristic, is the physical direction of an oscillating field in relation to the propagation direction.