Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. The phase velocity is not the velocity at which stu. 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. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics. The relation between group velocity and phase velocity are proportionate. Difference between phase velocity and group velocity velocity. Group and phase velocity up to now we have just talked about the speed or velocity v of a wave. A summary is presented of the correct interpretations of the phase velocity, ray velocity, and group velocity surfaces. Phase velocity and group velocity for beginners in the first section of this paper i derive the formulas for the phase velocity and group velocity as a function. Overlay the transparencies on the overhead projector and move one with respect to the other to demonstrate the difference between the phase velocity that of the transparency and the group velocity. Velocity with which the phase of a wave travels is called phase velocity. Kuzmichev recently showed that use of phase velocity rather than group velocity for cherenkov light signals and pulses from cali bration lasers. Group velocity, poynting and polarisation group velocity phase velocity is the rate of advance of constant phase surfaces. Group velocity and phase velocity university of british.
Opti 500 c, spring 2011, lecture 22, chromatic dispersion and pmd 2 phase and group velocity. 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 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 a capillary wave. Pdf phase velocity and group velocity in cylindrical and. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. The velocity of carrier wave is called the phase velocity. Phase and group velocity matching for cumulative harmonic generation in lamb waves article pdf available in journal of applied physics 1099. So, the phase velocity equals to the group velocity. What is the difference between phase velocity and group. In an anomalous medium, the group velocity is greater than the phase velocity. 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. Phase velocity and group velocity in engineering physics 2. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i.
The energy content in an infinite plane wave is obviously infinite, so we are more interested in finding the energy per unit area of the surface. But phase velocity really only applies to infinite time and space monochromatic sine waves these do not exist or if they do, are boring propagation of pulses. Pdf physical significance of the group velocity in dispersive. The distinction between the phase velocity and the group velocity of a wave is a concept of general signi cance for many di erent waves in physics.
The group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. Role of group and phase velocity in highenergy neutrino. 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. Closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. This is the group velocity and is which can be found if you have giving 7 v. A full set of computer generated plots of such surfaces are presented. The phase velocity, ray velocity, and group velocity surfaces for a. About the nonrelativistic limit of the phase velocity of. The group velocity is what has to be considered for the code measurements, i. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. Phase velocity and group velocity are two very important concepts in physics. The group velocity is the speed of the overall shape of a modulated wave called the envelope. A fundamental relation between phase 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. The velocity at which a single frequency of a wave group or a phase or part such as the crest or troughof a wave group travels through a medium. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. Phase velocity can exceed velocity of light in vacuum, c. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. The main difference between phase velocity and group velocity is that phase velocity is greater than the group velocity in a normal medium. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Relation between phase velocity and group velocity by education study. Particle waves and group velocity university of kansas. In contrast, the nonrelativistic phase velocity and the relativistic phase velocity are not. Group velocity when the various frequency components of a waveform have different phase velocities, the phase velocity of the waveform is an average of these velocities the phase velocity of the carrier wave, but the waveform itself moves at a different speed than the underlying carrier wave called the group velocity. Group velocity and phase velocity light speed is really the phase velocity v.
Opti 500 c, spring 2011, lecture 22, chromatic dispersion and pmd 3 phase and group velocity. Mungan, spring 2017 consider a beam of particles traveling in free space in the same direction with nonrelativistic speed find their quantummechanical phase velocity. Phase speed and group velocity, in the case of the linear advection equation, c and. The angle insider the cos term in a certain phase is.
Write each answer as a multiple of the speed of light c. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. In the presence of dispersion, the second term in the denominator. The group velocity is equal to the real velocity of the particle in both cases. Difference between phase velocity and 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. Phase velocity and group velocity in engineering physics 2 pdf free download the phase velocity and group velocity are speed in terms of an expression. The group velocity also has relation with the phase velocity. Pdf phase and group velocity matching for cumulative. 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. A wave of any shape will travel undistorted at this velocity. 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. This is really the velocity of the waves however information travels in wave packets wave packets have a frequency variation.
Relation between group velocity and phase velocity at byjus. Is it possible for a group velocity of any wave disturbance to be greater than its component phase. You can nd more information on the distinction between the phase velocity and the group velocity. This is the velocity at which the phase of any one frequency component of the wave travels. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. Here is a simple way to think about the difference. Description the two transparencies have sets of parallel lines with slightly different spacings. In order to understand the nature of the group velocity. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. This article tries to differentiate those differences in detail. Group velocity and phase velocity light speed is really.
The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wavefront. The nonrelativistic group velocity and the relativistic group velocity yield exactly the same result. The phase velocity, ray velocity, and group velocity surfaces for a magnetoionic medium volume 17 issue 3 a. Fundamental relation between phase and group velocity, and. It is explained and illustrated in this document, using little animations in the pdf le. 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. Phase velocity and group velocity as a function of the total relativistic energy and the relativistic momentum of a particle 2.
The group velocity and phase velocity relation can be mathematically written as. Phase velocity and group velocity in a wave packet 2 x. 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. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd.
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 such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number. Simultaneous negative phase and group velocity of light in. Phase velocity and group velocity as a function of the angular frequency and the wave number 4.
The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to. Sending a square pulse as a basic communication tool is the main focus of this lecture. Group and phase velocity wolfram demonstrations project. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. These are plotted and compared for orders 0, 1 and 2, but the expressions are. Flash and javascript are required for this feature. Relation between phase velocity and group velocity by. The phase velocity, ray velocity, and group velocity. Opti 500 c, spring 2011, lecture 22, chromatic dispersion and pmd 4.