Trigonometric functions {wave equation}| can describe waves. y = A * sin(2 * pi * f * t), where y is displacement, A is amplitude, f is frequency, and t is time. y = A * sin(2 * pi * x / l), where y is displacement, A is amplitude, x is position, and l is wavelength.
position and time
Wave equations are differential equations and include length and time. (D^2)H(x,t) / Dt^2 = (v^2) * (D^2)H(x,t) / Dx^2, where (D^2) indicates second partial derivative, H is function of displacement and time, v is wave velocity, x is position, and t is time. Solutions are waves. In springs, velocity depends on mass and material elasticity {spring constant, oscillation}. For strings, velocity depends on density, tension, and material. For solids, velocity depends on density and material elasticity {Young's modulus, oscillation}. For liquids, velocity depends on density and material elasticity {bulk modulus}. For gases, velocity depends on density, pressure, and molecule type: monatomic, diatomic, triatomic, and so on. For light, velocity depends on material magnetic permeability and electric permittivity.
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Date Modified: 2022.0224