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Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation, these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays.
The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. [37] Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters.
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.
Bessel functions describe the radial part of vibrations of a circular membrane.. Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation + + = for an arbitrary complex number, which represents the order of the Bessel function.
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration ...
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the ...
This later led to a series of articles (1959 to 1989) by Bondi and Pirani that established the existence of plane wave solutions for gravitational waves. [29] Paul Dirac further postulated the existence of gravitational waves, declaring them to have "physical significance" in his 1959 lecture at the Lindau Meetings. [30]