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Traveling Plane Wave
In mathematics and physics, a traveling plane wave is a special case of plane wave, namely a field (physics), field whose evolution in time can be described as simple translation of its values at a constant wave speed c, along a fixed direction of propagation \vec n. Such a field can be written as :F(\vec x, t)=G\left(\vec x \cdot \vec n - c t\right)\, where G(u) is a function of a single real parameter u = d - c t. The function G describes the profile of the wave, namely the value of the field at time t = 0, for each displacement d = \vec x \cdot \vec n. For each displacement d, the moving plane perpendicular to \vec n at distance d + c t from the origin is called a wavefront. This plane too travels along the direction of propagation \vec n with velocity c; and the value of the field is then the same, and constant in time, at every one of its points. The wave F may be a scalar field, scalar or vector field; its values are the values of G. A sinusoidal plane wave is a special ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
