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Sine waves occur often in physics, including wind waves, sound waves, and light waves, such as monochromatic radiation. In engineering , signal processing , and mathematics , Fourier analysis decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.
The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. the direction of the group velocity. For light waves in vacuum, this is also the direction of the Poynting vector. On the other hand, the wave vector points in the direction of phase velocity.
Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.
kinetic energy: joule (J) wave vector: radian per meter (m −1) Boltzmann constant: joule per kelvin (J/K) wavenumber: radian per meter (m −1) stiffness: newton per meter (N⋅m −1) ^ Cartesian z-axis basis unit vector unitless angular momentum
A looped animation of a wave packet propagating without dispersion: the envelope is maintained even as the phase changes. In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an envelope.
The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile () is a sinusoidal function. That is, (,) = (() +) The parameter , which may be a scalar or a vector, is called the amplitude of the wave; the scalar coefficient is its "spatial frequency"; and the scalar is its "phase shift".
By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x component for the x axis) of a vector wave without sources of waves ...
In physics, a mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a material medium. [1] Vacuum is, from classical perspective, a non-material medium, where electromagnetic waves propagate.)