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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.
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
Surface waves in water showing water ripples. In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency.
A trough is the opposite of a crest, so the minimum or lowest point of the wave. When the crests and troughs of two sine waves of equal amplitude and frequency intersect or collide, while being in phase with each other, the result is called constructive interference and the magnitudes double (above and below the line).
An undamped spring–mass system is an oscillatory system. Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
In most cases this is a longitudinal wave of pressure (such as sound), but it can also be a transverse wave, such as the vibration of a taut string. In the case of a sound wave travelling through air, the particle displacement is evident in the oscillations of air molecules with, and against, the direction in which the sound wave is travelling. [2]
Numerical simulation of the Fisher–KPP equation. In colors: the solution u(t,x); in dots : slope corresponding to the theoretical velocity of the traveling wave.. In mathematics, Fisher-KPP equation (named after Ronald Fisher [1], Andrey Kolmogorov, Ivan Petrovsky, and Nikolai Piskunov [2]) also known as the Fisher equation, Fisher–KPP equation, or KPP equation is the partial differential ...
Wave properties may refer to: Physical properties of waves : transmission, reflection, polarization, diffraction, refraction and others Mathematical description of waves : amplitude, frequency, wavelength, and others