Consider a wave packet as a function of position x and time t: α ( x, t ).

Consider a wave function that is a sum of many waves, however, we may write this as

Consider a traveling transverse wave ( which may be a pulse ) on a string ( the medium ).

Consider a light wave propagating along the z principal axis polarised such the electric field of the wave is parallel to the x-axis.

Consider solutions in which a fixed wave form ( given by f ( X )) maintains its shape as it travels to the right at phase speed c. Such a solution is given by ( x, t )

Consider the net electric field E produced by a light wave of frequency ω together with an external electric field E < sub > 0 </ sub >:

Consider a set of points R ( R is a vector depicting a point in a Bravais lattice ) constituting a Bravais lattice, and a plane wave defined by:

Consider an inertial observer in Minkowski spacetime who encounters a sandwich plane wave.

Consider a plane wave where all perturbed quantities vary as exp ( i ( kx-ωt )).

Consider, for example, a two element array spaced apart by one-half the wavelength of an incoming RF wave.

Consider a second order partial differential equation in three variables, such as the two-dimensional wave equation

Consider a space ship traveling from Earth to the nearest star system outside of our solar system: a distance years away, at a speed ( i. e., 80 percent of the speed of light ).

Consider a pulse of light traveling in glass.

Consider a car traveling on a straight line through a hilly road.

* rotary traveling wave oscillator.

Some exact solutions describe gravitational waves without any approximation, e. g., a wave train traveling through empty space or so-called Gowdy universes, varieties of an expanding cosmos filled with gravitational waves.

The ever expanding ring of waves is the wave group, within which one can discern individual wavelets of differing wavelengths traveling at different speeds.

If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,

Pressure waves or Primary waves ( P-waves ), are longitudinal waves that involve compression and rarefaction ( expansion ) in the direction that the wave is traveling.

The shock wave was traveling to the " Great Vibranium Mound " in Wakanda, where the resulting explosion could destroy the world.

It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.

A standing wave ( black ) depicted as the sum of two propagating waves traveling in opposite directions ( red and blue )

The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.

Consequently, wavelength, period, and wave velocity are related just as for a traveling wave.

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

In certain circumstances, waves of unchanging shape also can occur in nonlinear media ; for example, the figure shows ocean waves in shallow water that have sharper crests and flatter troughs than those of a sinusoid, typical of a cnoidal wave, a traveling wave so named because it is described by the Jacobi elliptic function of m-th order, usually denoted as.

If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave.

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).

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.

Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction ( refraction ) that results.