You can say that the velocity of the particle cant be higher than the speed of light without quantum mechanics, but then there is no group velocity. Nov 18, 2017 relation between phase velocity and group velocity learn only in 1. May 10, 2017 wave function, phase velocity, group velocity, plasma frequency. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Frequency dispersion in groups of gravity waves on the surface of deep water. Group velocity the phase velocity of a wave is and comes from the change in the position of the wavefronts as a function of time the waveform moves at a rate that depends on the relative position of the component wavefronts as a function of time. Group delay is the length of a circuit or transmission line, divided by its group velocity. Apr 15, 2016 for example, the phase velocity is equal to the group velocity when sound waves travel through the air as air is a non dispersive medium for sound waves. For airfilled waveguide, the phase velocity reduces further to. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. If we have two waves that are slightly di erent in frequency.
When phase velocity increases, proportionately group velocity will also increase. You can nd more information on the distinction between the. This is meant to serve as a general guide, as rock types are classified by a range of physical properties values which can lead to order of magnitude differences in phase velocity. Phase velocity definition of phase velocity by merriam. This is the group velocity and is which can be found if you have giving 7 v. Well the trick indeed is to recognise the two separate wave components and treat these for now as two separate waves and calculate their phase velocity ie the rate of movement of points of constant phase in each wave. The red dot overtakes two green dots when moving from the. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as. Simultaneous negative phase and group velocity of light in.
The simplest atmospheric waves are sinusoidal oscil lations that satisfy linearized forms of the dynamical equations. The relation between group velocity and phase velocity are. In the presence of dispersion, the second term in the denominator. The group velocity is what has to be considered for the code measurements, i. It can be understood as the change in velocity of the wave components of a sine wave, when modulated. Thus we see direct dependence of group velocity on phase velocity and viseversa. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. So, the phase velocity equals to the group velocity. Phase velocity and group velocity superposition of light waves when we analyze the resultant of two or more simple harmonic vibrations monochrome light waves, we usually can treat it as the simple sum of the individual vibrations waves as shown below.
You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a. Phase velocity and group velocity are two very important concepts in physics. The latter again is a function of the permittivity of the medium, we have already derived in chapter 3 the refractive index as a function of medium permittivity, given by n v. Phase velocity definition of phase velocity by merriamwebster. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. Since each amplitude envelope contains a group of internal waves, this speed is usually called the group velocity, vg. Velocity with which the phase of a wave travels is called phase velocity.
The table below shows phase velocity for certain rocks at various frequencies. Phase velocity and group velocity in a wave packet 2 x. In an anomalous medium, the group velocity is greater than the phase velocity. As a result, the peak of a temporally long gaussian. The phase velocity, ray velocity, and group velocity. Waves can be in the group and such groups are called as wave packets, so the velocity with a wave packet travels is called group velocity. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. According to the definition, the rate of phase change at 2. May 12, 2006 the group velocity v group can be expressed as. The phase velocity, ray velocity, and group velocity surfaces for a magnetoionic medium by a. The product of the phase velocity and the group velocity the product between the phase velocity and the group velocity of any particle massive or massless equals the square of the speed of light in vacuum. What are phase velocity, group velocity, and signal velocity.
For example, the phase velocity is equal to the group velocity when sound waves travel through the air as air is a non dispersive medium for sound waves. So how can one talk about a point of constant phase here to obtain the group velocity as it is a product of sin and cos. To begin, lets think about how to solve the wave equation in a dispersive system with initial condition ax,t0fx 9. The phase velocity is not the velocity at which stu. Difference between phase velocity and group velocity velocity.
The velocity of a wave can be defined in many different ways, partly because there many different kinds of waves, and partly because we can focus on different aspects or components of any given wave. Pdf phase velocity and group velocity in cylindrical and. It is this modulation that represents the signal content. Here is a simple way to think about the difference. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. Pdf closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. Wave function, phase velocity, group velocity, plasma frequency. Usually, group velocity is not equal to phase velocity, except in empty space. Calculate the group velocity of a relativistic particle. Group velocity is the speed at which electromagnetic information travels. What is the difference between phase velocity and group.
The red dot overtakes two green dots when moving from the left to the ri. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. The group velocity of a wave is the velocity with which the overall envelope shape of the waves amplitudesknown as the modulation or envelope of the wavepropagates through space. That is, to within a phase factor of unit modulus the waveform fx,t is a function of a single variable,x. Without quantum mechanics a particle is not considered a wave so there is no group velocity or phase velocity, only the velocity of the particle. The phase and group velocity of the wave is dependent upon the refractive index, n. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. Group velocity and phase velocity university of british. Note that in this particular case, both group and phase velocities are positive. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i.
Light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. Pdf on apr 1, 2019, joseph braat and others published phase and group velocity of a wave packet find, read and cite all the research you need on researchgate. This notes is meant to be a supplement and not a substitute for. We can obtain phase velocity from solving the wave equation. What is the relation between phase velocity and group. The phase velocity of an electrometric wave propagating in a hollow metallic rectangular waveguide in the te 10 mode is a equal to its group velocity b less than velocity of light in free space c equal to the velocity of light in free space. Phase and group velocities article pdf available in computer physics communications 207 june 2016 with 1,343 reads how we measure reads. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. The propagation of waves through dispersive media often leads to surprising or counterintuitive behavior. Dispersive medium, phase velocity, group velocity author.
They arise in quantum mechanics in the time development of the state function for the continuous case, i. Lecture 7 wave function, phase velocity, group velocity. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. Particle waves and group velocity university of kansas.
Suppose there is a series of ocean waves approaching the shore at an oblique angle that is, they are not coming in perpendicular to the shore line. The latter again is a function of the permittivity of the medium, we have already derived in chapter 3 the refractive index as a function of medium permittivity, given by n vas the permittivity of the medium is different from that of the vacuum, the waves move with different phase velocity in the. Pdf fundamental relation between phase and group velocity, and. The product between the phase velocity and the group velocity of any particle massive or massless equals the square of the speed of light in vacuum.
Pdf phase velocity and group velocity bs physics students. Joe khachan from the school of physics, the university of sydney. Up to now we have just talked about the speed or velocity v of a wave. The group velocity is directly proportional to phase velocity. Difference between phase velocity and group velocity. For debroglie mass waves, the particle frequency is a linear function of the particle energy e, so it is typical to write the group velocity in the following form.
Relation between phase velocity and group velocity learn only in 1. The resulting wave packet travels with the socalled group velocity which is faster than the phase velocity in this case. Phase velocity is the rate at which the wave changes its phase in order to undergo a phase shift of 2. Assume a particle of mass m and traveling with a speed of v. Sending a square pulse as a basic communication tool is the main focus of this lecture. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics. Feb 16, 2019 here is a simple way to think about the difference. Phase velocity and group velocity in a wave packet phase velocity. This is the velocity at which the phase of any one frequency component of the wave travels. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. A onedimensional harmonic wave figure 1 is described by the equation. From this you can see that when the cutoff frequency is reached, the phase velocity goes to infinity.
For the case of positiverefractiveindex media in electrodynamics, where the phase velocity v phase is positive in the forward direction, the group velocity v group can become negative in the regime of anomalous dispersion. Walker department of physics, university of natal, durban, 4001, south africa received 22 june 1976 and in revised form 25 october 1976 the phase velocity surface for. The wave packet envelope is shown in magenta color in dashed lines. Pdf we demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. The speed of the monochromatic wave is just the phase velocity of the main wave. Phase velocity definition is the velocity of a wave motion as determined by the product of the wavelength and frequency called also wave velocity. Relation between group velocity and phase velocity at byjus. Relation between phase velocity and group velocity. Then, to obtain the wave equation, we need to consider the maxwells equation. In the context of gnss signals, the carrier waves are propagating with the phase velocity and thence, this is the velocity associated to the carrier measurements. Fundamental relation between phase and group velocity, and. A fundamental relation between phase and group velocity, and. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g.
In this deepwater case, the phase velocity is twice the group velocity. Calculate the phase velocity of a relativistic particle. This result follows directly from the groupvelocity equations 1. The group velocity is usually the more important physical velocity, since it determines how fast the energy in the wave packet propagates, or in quantum mechanics, how quickly the expectation value for the position of a particle moves. Simultaneous negative phase and group velocity of light in a. Phase and group velocity are two important and related concepts in wave mechanics. The distinction between the phase velocity and the group velocity of a wave is a concept of.
1004 688 1195 850 1050 907 1007 403 1607 253 925 169 303 1262 213 374 538 420 1519 361 777 1487 551 890 1237 431 753 613 506 859 1210 539 333 637