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From the basic one-dimensional plane-wave solutions, a general form of a wave packet can be expressed as (,) = (()). where the amplitude A(k), containing the coefficients of the wave superposition, follows from taking the inverse Fourier transform of a "sufficiently nice" initial wave u(x, t) evaluated at t = 0: = (,) . and / comes from Fourier ...
JEE (Advanced) is conducted in two papers of three hours each – Paper-1 and Paper-2 (both compulsory) consist of questions from three major subjects: physics, chemistry and mathematics. Unlike most of the other exams, the type, the number of questions being asked in the paper, the total marks and the marking scheme varies from year to year ...
The wave equation alone does not specify a physical solution; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the amplitude and phase of the wave. Another important class of problems occurs in enclosed spaces specified by boundary conditions, for which the solutions ...
Left: the real part of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts. Out of phase AE. A real-world example of a sonic phase difference occurs in the warble of a Native American flute.
Solitary wave in a laboratory wave channel. In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets.
Dispersion occurs when sinusoidal waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave, v {\displaystyle v} , is a function of the wave's wavelength λ {\displaystyle \lambda } :
These waves travel in vacuum at the speed of light and exist in a wide spectrum of wavelengths. Examples of the dynamic fields of electromagnetic radiation (in order of increasing frequency): radio waves , microwaves , light ( infrared , visible light and ultraviolet ), x-rays and gamma rays .
Partial-wave analysis, in the context of quantum mechanics, refers to a technique for solving scattering problems by decomposing each wave into its constituent angular-momentum components and solving using boundary conditions.