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The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. [1] [2] [3] The Doppler effect is named after the physicist Christian Doppler, who described the phenomenon in 1842.
The phase velocity c p (blue) and group velocity c g (red) as a function of water depth h for surface gravity waves of constant frequency, according to Airy wave theory. Quantities have been made dimensionless using the gravitational acceleration g and period T, with the deep-water wavelength given by L 0 = gT 2 /(2π) and the deep-water phase ...
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.
In a dispersive medium, the speed of sound is a function of sound frequency, through the dispersion relation. Each frequency component propagates at its own speed, called the phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves; see optical dispersion for a description.
Frequency dispersion of surface gravity waves on deep water. The red square moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square traverses the figure in the time it takes the green dot to traverse half.
Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between signal cycles) with respect to a reference. [3]
Using this frequency, the Bode phase plot finds the phase of βA OL. If the phase of βA OL (f 0 dB) > −180°, the instability condition cannot be met at any frequency (because its magnitude is going to be < 1 when f = f 180), and the distance of the phase at f 0 dB in degrees above −180° is called the phase margin.
= is the escape velocity, and β e = v e / c {\displaystyle \beta _{e}=v_{e}/c} is the escape velocity, expressed as a fraction of the speed of light c. To illustrate then, without accounting for the effects of rotation, proximity to Earth's gravitational well will cause a clock on the planet's surface to accumulate around 0.0219 fewer seconds ...