The second factor slides rigidly to the right with the phase velocity vphase u. This is the socalled dispersion relation for the above wave equation. Light waves in the vacuum have the special property that the velocity is exactly the. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. Given below are examples of wave equations in 3 dimensions for. By using an empirical expression relating the rate of increase in wave energy to the local wind speed, an equation for the phase speed at the peak of the wave spectrum is derived.
Any superposition of these pure waves will always be some function of the. Pdf phase velocity and group velocity in cylindrical and. Wave function, phase velocity, group velocity, plasma frequency. The phase and group velocity of the wave is dependent upon the refractive index, n. Recall the governing equations for pressure and velocity. In the x, t plane, v has a constant value along a line of contant phase. Lecture 7 wave function, phase velocity, group velocity. As will be shown later, the phase speed of the fastest wave is. Untitled erhard wielandts website for free seismological software. Dispersion characteristics of these waves are examined and discussed.
The phase velocity of tail waves is equal to the soliton velocity, while their group velocity. The implications for thermodynamic applicability of the wave equation and for application. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. A onedimensional harmonic wave figure 1 is described by the equation. Eikonal equation, phase velocity, polar phase shift, structural inter pretation, surface waves, wave equation. We can obtain phase velocity from solving the wave equation. Traffic flow waves small local changes in velocity occurring in high density. The latter again is a function of the permittivity of the medium, we have. Let us first give a quick derivation of the mathematical result.