Propagation constant a conductor. The skin effect causes R along the conductor to be approximately dependent on frequency according to Losses in the dielectric depend on the loss tangent (tan "δ") of the material divided by the wavelength of the signal. Thus they are directly proportional to the frequency. The attenuation constant for a particular propagation mode in an optical fiber is the real part of the axial propagation constant. In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave. It represents the change in phase
Acoustic wave equation include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article or the survey paper. The wave equation describing sound in one dimension (position formula_3) is where formula_1 is the acoustic pressure (the local deviation from the ambient pressure), and where formula_6 is the speed of sound. Provided that the speed formula_6 is a constant, not dependent on frequency (the dispersionless case), then the most general solution is where formula_9 and formula_10 are any two twice-differentiable functions. This may be pictured as the superposition of two waveforms of arbitrary profile, one (formula_9) travelling up the x-axis