Wave

If the relative amplitude of oscillation at different points in the field remains constant, the wave is said to be a standing wave. On the other hand, some waves do not appear to move at all, like standing waves (which are fundamental to music) and hydraulic jumps.

In physics, a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space.

The types of waves most commonly studied in physics are mechanical and electromagnetic.

A mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium.

Some, like the probability waves of quantum mechanics, may be completely static.

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be measured (the uncertainty principle).

A plane wave can be a transverse, if its effect at each point is described by a vector that is perpendicular to the direction of propagation or energy transfer; or longitudinal, if the describing vectors are parallel to the direction of energy propagation.

In physics, a transverse wave is a moving wave whose oscillations are perpendicular to the direction of the wave.

A plane wave seems to travel in a definite direction, and has constant value over any plane perpendicular to that direction.

In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space.

For example, sound waves in air are variations of the local pressure that propagate by collisions between gas molecules.

Other types of waves include gravitational waves, which are disturbances in a gravitational field that propagate according to general relativity; heat diffusion waves; plasma waves, that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.

The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons.

Other types of waves include gravitational waves, which are disturbances in a gravitational field that propagate according to general relativity; heat diffusion waves; plasma waves, that combine mechanical deformations and electromagnetic fields; reaction-diffusion waves, such as in the Belousov–Zhabotinsky reaction; and many more.

This complex of particles and fields supports a wide variety of wave phenomena.

In physics, mathematics, and related fields, a wave is a disturbance (change from equilibrium) of one or more fields such that the field values oscillate repeatedly about a stable equilibrium (resting) value.

Waves can be constructed as physical fields, due to their finite propagation speed and causal nature when a simplified physical model of an isolated closed system is set.

On the other hand, some waves do not appear to move at all, like standing waves (which are fundamental to music) and hydraulic jumps.

When this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves.

Yet this small change makes a huge difference on the set of solutions F. This differential equation is called "the" wave equation in mathematics, even though it describes only one very special kind of waves.

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.

If the group velocity v_g (see below) is wavelength-independent, this equation can be simplified as: There are two velocities that are associated with waves, the phase velocity and the group velocity.

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.

where A(x,\ t) is the amplitude envelope of the wave, k is the wavenumber and \phi is the phase.

In the physical sciences, the wavenumber (also wave number or repetency ) is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.

Phase velocity is the rate at which the phase of the wave propagates in space: any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.

Wave propagation is any of the ways in which waves travel.

There are two velocities that are associated with waves, the phase velocity and the group velocity.

The phase velocity of a wave is the rate at which the phase of the wave propagates in space.

Phase velocity is the rate at which the phase of the wave propagates in space: any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.

A crest is the point on a wave with the maximum value of upward displacement within a cycle.

This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions.

In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude.

Wavelength can be a useful concept even if the wave is not periodic in space.

Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity.

The quantity is the wavelength of the emitted note, and is its frequency.) Many general properties of these waves can be inferred from this general equation, without choosing specific values for the parameters.

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time.

The directions of incidence and refraction are related to the refractive indices of the two materials by Snell's law.

Snell's law (also known as Snell-Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

The quantity is the wavelength of the emitted note, and is its frequency.) Many general properties of these waves can be inferred from this general equation, without choosing specific values for the parameters.

Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition.

The amount by which a wave is refracted by a material is given by the refractive index of the material.

It can also be applied to wave phenomena such as sound.

The speed of a transverse wave traveling along a vibrating string ( v ) is directly proportional to the square root of the tension of the string ( T ) over the linear mass density :

A vibration in a string is a wave.

In particular, many media are linear, or nearly so, so the calculation of arbitrary wave behavior can be found by adding up responses to individual sinusoidal waves using the superposition principle to find the solution for a general waveform.

Fourier analysis is particularly common for waves.

In physics and engineering, a ripple tank is a shallow glass tank of water used in schools and colleges to demonstrate the basic properties of waves.