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A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2] which uses the trigonometric formula for the addition of ...
A standing wave, also known as a stationary wave, is a wave whose envelope remains in a constant position. This phenomenon arises as a result of interference between two waves traveling in opposite directions. The sum of two counter-propagating waves (of equal amplitude and frequency) creates a standing wave. Standing waves commonly arise when ...
Wave packet. 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. A wave packet can be analyzed into, or can be ...
An envelope detector is sometimes referred to as an envelope follower in musical environments. It is still used to detect the amplitude variations of an incoming signal to produce a control signal that resembles those variations. However, in this case the input signal is made up of audible frequencies.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Wave refraction in the manner of Huygens Wave diffraction in the manner of Huygens and Fresnel. The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. [1]
Fourier optics begins with the homogeneous, scalar wave equation (valid in source-free regions): (,) = where is the speed of light and u(r,t) is a real-valued Cartesian component of an electromagnetic wave propagating through a free space (e.g., u(r, t) = E i (r, t) for i = x, y, or z where E i is the i-axis component of an electric field E in the Cartesian coordinate system).
Beat (acoustics) In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. With tuning instruments that can produce sustained tones, beats can be readily recognized.
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