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:
“Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
—Honoré De Balzac (1799–1850)
“There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
—Umberto Eco (b. 1932)
“The conflict between the need to belong to a group and the need to be seen as unique and individual is the dominant struggle of adolescence.”
—Jeanne Elium (20th century)
“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)
“For myself and my loved ones, I want the heat, which comes at the speed of light. I don’t want to have to hang about for the blast, which idles along at the speed of sound.”
—Martin Amis (b. 1949)