Since the 1980s, various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum.

Since ω = − dΦ / dt and k = + dΦ / dx, the wave velocity is v = dx / dt = ω / k.

Since each amplitude envelope contains a group of internal waves, this speed is usually called the group velocity.

Since the particle speed < math > v < c </ math > for any particle that has mass ( according to special relativity ), the phase velocity of matter waves always exceeds c, i. e.

Since the phase velocity is lower in the second medium ( v < sub > 2 </ sub > < v < sub > 1 </ sub >), the angle of refraction θ < sub > 2 </ sub > is less than the angle of incidence θ < sub > 1 </ sub >; that is, the ray in the higher-index medium is closer to the normal.

Since the elevator would attain orbital velocity as it rode up the cable, an object released at the tower's top would also have the orbital velocity necessary to remain in geostationary orbit.

Since a laser can heat propellant to extremely high temperatures, this potentially greatly improves the efficiency of a rocket, as exhaust velocity is proportional to the square root of the temperature.

Since that fuel must itself be accelerated, this results in an approximately exponential increase in mass as a function of velocity change at non-relativistic speeds, asymptotically tending to infinity as it approaches the speed of light.

Since the values for drag are based on relative velocity, using the scoop as a form of electromagnetic sail will provide additional thrust as long as the vessel is travelling at less than 500, 000 m / s away from a star.

Since power varies with the cube of velocity, the power required for the operation is also less.

Since wave phase velocity is given by ;

Since the size and direction of the tin whistle's windway is fixed, like that of the Recorder or fipple flute, it is necessary to increase the velocity of the air stream.

Since the velocity is lower in the second medium ( v < sub > 2 </ sub > < v < sub > 1 </ sub >), the angle of refraction θ < sub > 2 </ sub > is less than the angle of incidence θ < sub > 1 </ sub >; that is, the ray in the higher-index medium is closer to the normal.

Since light always moves at a constant speed, lensing changes the direction of the velocity of the light, but not the magnitude.

Since thrust depends on both the amount of gas moved and the velocity, we can generate high thrust by accelerating a large mass of gas by a small amount, or by accelerating a small mass of gas by a large amount.

Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field ; this leads to Ohm's law.

Since longitudinal waves have a much greater phase velocity than transverse waves, V < sub > long </ sub > is much greater than V < sub > trans </ sub >, and the relaxation length or mean free path of longitudinal phonons will be much greater.

Since kinetic energy increases quadratically with velocity (), an object moving at 10 m / s has 100 times as much energy as one of the same mass moving at 1 m / s, and consequently the theoretical braking distance, when braking at the traction limit, is 100 times as long.

Since point P and O < sub > 2 </ sub > have only one velocity,

Since this definition does not specify velocity, it also applies to objects initially moving upward

Since in order to reach an object in orbit it is necessary to attain an extremely high velocity, their released kinetic energy alone is enough to destroy their target ; explosives are not necessary.

Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.

Since the planet is moving left at speed U, the total velocity of the rocket relative to the observer will be the velocity of the moving planet plus the velocity of the rocket with respect to the planet.

Since the Supreme Court's decision of that year this is more doubtful ; ;

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.

Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the difficulty of drawing the net is great, we will merely discuss it.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since the apparatus is new, it requires experimentation and changes in technique.

Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.