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In physics, a plane wave is a special case of a wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. [1] For any position in space and any time , the value of such a field can be written as (,) = (,), where is a unit-length vector, and (,) is a function ...
This plane lies at distance from the origin when =, and travels in the direction ^ also with speed ; and the value of the field is then the same, and constant in time, at every one of its points. A sinusoidal plane wave could be a suitable model for a sound wave within a volume of air that is small compared to the distance of the source ...
By definition, all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. [8] The norm of a vector v in a normed vector space can be considered to be the magnitude of v.
For the Earth, this could have been an external magnetic field. Early in its history the Sun went through a T-Tauri phase in which the solar wind would have had a magnetic field orders of magnitude larger than the present solar wind. [60] However, much of the field may have been screened out by the Earth's mantle.
The angle can change over time due to polar wandering. Magnetic north is the direction that the north end of a magnetized compass needle points, which corresponds to the direction of the Earth's magnetic field lines. True north is the direction along a meridian towards the geographic North Pole.
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
A scale factor, (conventionally called the speed-of-light) relates distances measured in space to distances measured in time. The magnitude of this scale factor (nearly 300,000 kilometres or 190,000 miles in space being equivalent to one second in time), along with the fact that spacetime is a manifold, implies that at ordinary, non ...
Coordinate systems in astronomy can specify an object's relative position in three-dimensional space or plot merely by its direction on a celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth.