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[2] Another physical setting for derivation of the wave equation in one space dimension uses Hooke's law. In the theory of elasticity, Hooke's law is an approximation for certain materials, stating that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress).
In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and ...
Maxwell's equations can directly give inhomogeneous wave equations for the electric field E and magnetic field B. [1] Substituting Gauss's law for electricity and Ampère's law into the curl of Faraday's law of induction, and using the curl of the curl identity ∇ × (∇ × X) = ∇(∇ ⋅ X) − ∇ 2 X (The last term in the right side is the vector Laplacian, not Laplacian applied on ...
n (x) with n = −0.5 in the complex plane from −2 − 2i to 2 + 2i Plot of the Hankel function of the second kind H (2) n (x) with n = −0.5 in the complex plane from −2 − 2i to 2 + 2i. Another important formulation of the two linearly independent solutions to Bessel's equation are the Hankel functions of the first and second kind, H (1 ...
For such an antenna, the near field is the region within a radius r ≪ λ, while the far-field is the region for which r ≫ 2 λ. The transition zone is the region between r = λ and r = 2 λ . The length of the antenna, D, is not important, and the approximation is the same for all shorter antennas (sometimes idealized as so-called point ...
Discrete dipole approximation (DDA), also known as coupled dipole approximation, [1] is a method for computing scattering of radiation by particles of arbitrary shape and by periodic structures. Given a target of arbitrary geometry, one seeks to calculate its scattering and absorption properties by an approximation of the continuum target by a ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
An example application of the Fourier transform is determining the constituent pitches in a musical waveform.This image is the result of applying a constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord.