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Doppler shift of the direct path can be estimated by the following formula: [22], = where is the speed of the mobile station, is the wavelength of the carrier, is the elevation angle of the satellite and is the driving direction with respect to the satellite.
The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As a result, the change in direction upon entering a different medium changes with the wavelength of the wave. For electromagnetic waves the speed in a medium is governed by its refractive index according to
The phase speed – and thus also the wavelength L = c p T – decreases monotonically with decreasing depth. However, the group velocity first increases by 20% with respect to its deep-water value (of c g = 1 / 2 c 0 = gT/(4π)) before decreasing in shallower depths. [1]
The wavefront moves with speed , but at the same time the receiver moves away with speed during a time ,, which is the period of light waves impinging on the receiver, as observed in the frame of the source.
The phase velocity is the speed at which the crests or the phase of the wave moves, ... where the refractive index increases with wavelength. [27]
The top electron has twice the momentum, while the bottom electron has half. Note that as the momentum increases, the phase velocity decreases down to c, whereas the group velocity increases up to c, until the wave packet and its phase maxima move together near the speed of light, whereas the wavelength continues to decrease without bound. Both ...
Using another normalization for the same frequency dispersion relation, the figure on the right shows that for a fixed wavelength λ the phase speed c p increases with increasing water depth. [1] Until, in deep water with water depth h larger than half the wavelength λ (so for h/λ > 0.5), the phase velocity c p is independent of the water ...
The relevant wave speed in the discussion above is the phase velocity of the wave. This is typically close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction.