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The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as ... (where the wave speed is c 2 ...
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
The standard equations for the speed of sound apply with reasonable accuracy only to situations in which the wavelength of the sound wave is considerably longer than the mean free path of molecules in a gas.
v = speed of sound, ... Wave equation General solution/s Non-dispersive Wave Equation in 3d A = amplitude as function of position and time
The wave equation describing a standing wave field in one dimension (position ) is p x x − 1 c 2 p t t = 0 , {\displaystyle p_{xx}-{\frac {1}{c^{2}}}p_{tt}=0,} where p {\displaystyle p} is the acoustic pressure (the local deviation from the ambient pressure) and c {\displaystyle c} the speed of sound , using subscript notation for the partial ...
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 .
Depending on the wave equation, the wave packet's profile may remain constant ... where r is the distance from the origin, the speed of the particle is zero, ...
with T the wave period (the reciprocal of the frequency f, T=1/f). So in deep water the phase speed increases with the wavelength, and with the period. Since the phase speed satisfies c p = λ/T = λf, wavelength and period (or frequency) are related. For instance in deep water: