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While periodic travelling waves have been known as solutions of the wave equation since the 18th century, their study in nonlinear systems began in the 1970s. A key early research paper was that of Nancy Kopell and Lou Howard [1] which proved several fundamental results on periodic travelling waves in reaction–diffusion equations.
Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at ...
In seismology, shear waves are also called secondary waves or S-waves. Transverse waves are contrasted with longitudinal waves , where the oscillations occur in the direction of the wave. The standard example of a longitudinal wave is a sound wave or "pressure wave" in gases, liquids, or solids, whose oscillations cause compression and ...
As a wave, light is characterized by a velocity (the speed of light), wavelength, and frequency. As particles, light is a stream of photons . Each has an energy related to the frequency of the wave given by Planck's relation E = hf , where E is the energy of the photon, h is the Planck constant , 6.626 × 10 −34 J·s, and f is the frequency ...
Unguided electromagnetic waves in free space, or in a bulk isotropic dielectric, can be described as a superposition of plane waves; these can be described as TEM modes as defined below. However in any sort of waveguide where boundary conditions are imposed by a physical structure, a wave of a particular frequency can be described in terms of a ...
The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. Radio waves, at the low-frequency end of the spectrum, have the lowest photon energy and the longest wavelengths—thousands of kilometers, or more.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle . [ 1 ]