Relation To Group Velocity, Refractive Index and Transmission Speed
Since a pure sine wave cannot convey any information, some change in amplitude or frequency, known as modulation, is required. By combining two sines with slightly different frequencies and wavelengths,
the amplitude becomes a sinusoid with phase speed of vg = Δω/Δk. It is this modulation that represents the signal content. Since each amplitude envelope contains a group of internal waves, this speed is usually called the group velocity. In reality, the vp = ω/k and vg = dω/dk ratios are determined by the media. The relation between phase speed, vp, and speed of light, c, is known as refractive index, n = c/vp = ck/ω. Taking the derivative of ω = ck/n, we get the group speed,
Noting that c/n = vp, this shows that group speed is equal to phase speed only when the refractive index is a constant: dn/dk = 0. Otherwise, when the phase velocity varies with frequency, velocities differ and the medium is called dispersive. The phase velocity of electromagnetic radiation may – under certain circumstances (for example anomalous dispersion) – exceed the speed of light in a vacuum, but this does not indicate any superluminal information or energy transfer. It was theoretically described by physicists such as Arnold Sommerfeld and Léon Brillouin. See dispersion for a full discussion of wave velocities.
Read more about this topic: Phase Velocity
Famous quotes containing the words relation to, relation, group, index and/or speed:
“The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.”
—Sigmund Freud (1856–1939)
“Unaware of the absurdity of it, we introduce our own petty household rules into the economy of the universe for which the life of generations, peoples, of entire planets, has no importance in relation to the general development.”
—Alexander Herzen (1812–1870)
“...Women’s Studies can amount simply to compensatory history; too often they fail to challenge the intellectual and political structures that must be challenged if women as a group are ever to come into collective, nonexclusionary freedom.”
—Adrienne Rich (b. 1929)
“Exile as a mode of genius no longer exists; in place of Joyce we have the fragments of work appearing in Index on Censorship.”
—Nadine Gordimer (b. 1923)
“The correct rate of speed in innovating changes in long-standing social customs has not yet been determined by even the most expert of the experts. Personally I am beginning to think there is more danger in lagging than in speeding up cultural change to keep pace with mechanical change.”
—Mary Barnett Gilson (1877–?)