Group velocityThe 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. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group or wave packet, within which one can discern individual waves that travel faster than the group as a whole.
Phase velocityThe phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber (or angular wave number) k, which represent the angular change per unit of space, To gain some basic intuition for this equation, we consider a propagating (cosine) wave A cos(kx − ωt).
Speed of lightThe speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to ). According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects.
Angular velocityIn physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
Faster-than-lightFaster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (c). The special theory of relativity implies that only particles with zero rest mass (i.e., photons) may travel at the speed of light, and that nothing may travel faster. Particles whose speed exceeds that of light (tachyons) have been hypothesized, but their existence would violate causality and would imply time travel.
Light railLight rail transit (LRT) is a form of passenger urban rail transit characterized by a combination of tram and rapid transit features. While its rolling stock is similar to a traditional tram, it operates at a higher capacity and speed, and often on an exclusive right-of-way. In many cities, light rail transit systems more closely resemble, and are therefore indistinguishable from, traditional underground or at-grade subways and heavy-rail metros.
Velocity-addition formulaIn relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
LightLight or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). In physics, the term "light" may refer more broadly to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, microwaves and radio waves are also light.
Signal velocityThe signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated (using any particular method) between two separated parties. No signal velocity can exceed the speed of a light pulse in a vacuum (by Special Relativity). Signal velocity is usually equal to group velocity (the speed of a short "pulse" or of a wave-packet's middle or "envelope"). However, in a few special cases (e.g.
