For airfilled waveguide, the phase velocity reduces further to. When a wave is dispersive, a wavepacket will change shape as it propagates. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. The wavenumber k can be considered as the change in spectral phase per unit length the group velocity is the velocity with which the envelope of a pulse propagates in a medium, assuming a long pulse with narrow bandwidth so that higherorder chromatic dispersion is not relevant and the absence of nonlinear effects i. 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. The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to. We can obtain phase velocity from solving the wave equation. From this you can see that when the cutoff frequency is reached, the phase velocity goes to infinity. Relation between group velocity and phase velocity we know that phase velocity is given by. So, the phase velocity equals to the group velocity.
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. Phase and group velocity matching for cumulative harmonic generation in lamb waves article pdf available in journal of applied physics 1099. Phase velocity can exceed velocity of light in vacuum, c. Difference between phase velocity and group velocity velocity. This is the velocity at which the phase of any one frequency component of the wave travels. The difference between the group and phase velocity vectors may be caused by velocity variations with either frequency velocity dispersion or angle anisotropy. The velocity of component waves of a wave packet is called the phase velocity of those waves.
The group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. Relation between group velocity and phase velocity. Nov 18, 2017 relation between phase velocity and group velocity learn only in 1. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. The relation between group velocity and phase velocity are proportionate. The envelope of a wave packet see figure on right will travel at the group velocity, while the individual peaks and troughs within the envelope will move at the phase velocity. Sending a square pulse as a basic communication tool is the main focus of this lecture. Lets assume that some channel has same group velocity and phase velocity then does this mean that group delay and phase delay are same for that channel. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Relationship between group velocity and group delay. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics.
The speed of the wave packets is called the group velocity. Flash and javascript are required for this feature. Derive an expression for the angle a between the phase velocity and the group velocity. You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a. 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. 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 which are directly equal to each other. In contrast, the nonrelativistic phase velocity and the relativistic phase velocity are not only different between them and different from the real velocity, but also the. The phase velocity is the speed at which one member of the phase group travels. Going back to the case of airfilled waveguide, the group velocity is. Relation between group and particle velocity a material particle in motion is equivalent to a group of waves or wave packet.
For a free particle, is the group velocity equal to the phase velocity. Phase velocity and group velocity, relation between phase. Group velocity and phase velocity mathematics stack exchange. The velocity with which variation in the amplitude is transmitted represents the group velocity, and is given by. Relation between phase velocity and group velocity. Simultaneous negative phase and group velocity of light in. So vg is the partial derivative of relationship between group velocity vg and phase velocity vp. Relation between phase and group velocity engineering. Jan 20, 20 the resulting wave packet travels with the socalled group velocity which in the above case is faster than the phase velocity. Pdf fundamental relation between phase and group velocity, and.
The angle insider the cos term in a certain phase is. Interference of two sinusoidal waves with slightly different wavelengths, but the same amplitude and propagation direction, results in a beat pattern, called a wave group. The wave packet envelope is shown in magenta color in dashed lines. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n c v p ck. Phase velocity and group velocity in engineering physics 2. A fundamental relation between phase and group velocity. Group delay is the length of a circuit or transmission line, divided by its group velocity. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity.
Pdf phase and group velocity matching for cumulative. Review of basic formulas for waves in spacetime x,t or perspacetime. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. This is why group velocity is the more interesting quantity as it represents the velocity of information transmission in contrast, a single wavelength, cw beam carries no. The group velocity is the speed of the overall shape of a modulated wave called the envelope. Comparison between phase velocity and group velocity in the previous exercise, we have seen a case where the group and phase velocities are equal. From the equation 1 it is clear that the group velocity equals phase velocity if the term in the relationship between v g and phase velocity is. Assume a particle of mass m and traveling with a speed of v. Relation between phase velocity and group velocity by. Relation between group velocity and phase velocity at byjus. The relation between phase and group velocity is given by, vg. They arise in quantum mechanics in the time development of the state function for the continuous case, i. Calculate the phase velocity of a relativistic particle. Relation between group velocity and phase 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.
Oct 26, 2005 what i dont understand is why phase velocity does not carry informationenergy where as group velocity does. Phase velocity and group velocity, relation between phase velocity and group velocity. Then, to obtain the wave equation, we need to consider the maxwells equation. It is not just equal to the derivative, it wont even make sens dimensionally. General theorems on the equivalence of group velocity and. Phase velocity and group velocity, relation between phase velocity and group velocity duration. Group velocity, poynting and polarisation group velocity phase velocity is the rate of advance of constant phase surfaces. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. Group and phase velocities in the r theory of matter waves. The inequality of group velocity, speed of light in vacuum, and phase velocity is then. As can be seen in the animation, the group moves with a group velocity c g different from the phase velocity c p, due to frequency dispersion the group velocity is depicted by the red lines marked b in the two.
Nov 01, 2005 phase and group angles and velocities in anisotropic wave propagation the phase angles and velocities are different from the group angles and velocities. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. It is also important to remark that while the relativistic phase velocity is. Apr 03, 2016 in non dispersive medium, the group velocity is identical to phase velocity. Phase velocity and group velocity civil engineering ce. Pdf we demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. It looks as if the group velocity is the derivative of phase velocity but i dont think i am correct. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. Note that the group velocity is a bit slower than the phase velocity of the individual waves.
The conditions and sample solutions for superluminal signalling are given. 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. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. I look at it as k wave number approaching 0 so wavelength goes to infinity. 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. The relationship between the group velocity and phase velocity is, here, v phase represents the phase velocity. Calculate the group velocity of a relativistic particle. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the group velocity and is which can be found if you have giving 7 v. In the top left is a group that moves at the same velocity as the individual wave that makes it. This is typical for normal dispersion, where the speed of waves decreases as frequency increases. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n cv p ck.
Fundamental relation between phase and group velocity, and. Similarly we can get the group velocity vg by keeping the amplitude a constant. Following the same steps, we get the group velocity of the superposed 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. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. This site will allow you to access content of engineering physics syllabus of peoples university,related assignments, attendence and stay informed in recent activities in physics. It can be seen that this implies that group velocity is less than the speed of light, while phase velocity is greater than the speed of light. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures. In nondispersive materials, opposite group and phase velocity corresponds to. The group velocity by its definition vgdwkdk wk is known as the dispersion relation of the medium accounts for the fact that the refractive index varies over the bandwidth of the modulated wave.
A fundamental relation between phase and group velocity, and. Phase velocity and group velocity are two very important concepts in physics. The group velocity is simply the derivative of frequency. The group velocity can be very different from the phase velocity, only when the phase velocity has a very large derivative. Phase velocity definition of phase velocity by merriamwebster.
To construct this modulated wave need a wave packet made up of an. For a free particle, is the group velocity equal to the. Group velocity and phase velocity university of british. In order to go deeper, lets recall the definition of group velocity and lets give it a more interesting meaning by relating the concept with the transmission of information. Rp photonics encyclopedia group velocity, light, envelope. About the nonrelativistic limit of the phase velocity of. Schuster with noting in 1904 that a negative group velocity, i. To remove the flaws, a modified definition is proposed. Group, velocity, phase velocity and dispersion in a wave packet. Ece theory, r theory, group and phase velocity in r theory, superluminal signalling. Usually, group velocity is not equal to phase velocity, except in empty space. The group velocity is the velocity of the wave with lower frequency, but the phase velocity is the velocity of the wave with higher frequency. Introduction the concept of the group velocity of waves was introduced by hamilton in the.
The kinematic definition of group velocity uses the concept of stationary phase, and the velocity of energy pro pagation is defined as the energy ffux divided by the energy density. The classical definition of group velocity has two flaws. Group velocity is less than velocity of electromagnetic waves in free space. Relationship between phase velocity and group velocity. The group velocity is the speed of the constructed wave, created the group of waves. Relation between group and particle velocity engineering. Group velocity and phase velocity of the electromagnetic waves is the same in free space. The difference between group velocity and phase velocity is most relevant for light that is modulated at high frequencies or for pulses of light. In an anomalous medium, the group velocity is greater than the phase velocity. Phase and group velocity are two important and related concepts in wave mechanics. Well, in vacuum the group velocity and phase velocity are identical. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i. Group velocity is the speed at which electromagnetic information travels. The phase velocity is not the velocity at which stu.
Fundamental relation between phase and group velocity. Relation between phase velocity and group velocity learn only in 1. More generally, this relationship including the case of dispersive and negativeindex materials offers a perspective on the phenomena of backward waves and lefthanded media. 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. Waves on deep water with surface tension t and density. Derive an expression for the group velocity of the extraordinary wave in a uniaxial crystal as a function of the polar angle 0 of the propagation vector. Difference between phase velocity and group velocity. Phase velocity and group velocity as a function of the total.
Difference between phase and group velocity physics youtube. Particle waves and group velocity university of kansas. 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. This is the socalled dispersion relation for the above wave equation. I am getting confused between the concept of group velocity vs. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. This angle is also the angle between the field vectors e. Here is a simple way to think about the difference. The group velocity can be related to the derivative of phase velocity in respect to k or.
Modified definition of group velocity and electromagnetic. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. 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. A onedimensional harmonic wave figure 1 is described by the equation. To me, it doesnt make much sense what it means for phase velocity to exceed c.
Velocity with which the phase of a wave travels is called phase velocity. Group velocity, phase velocity, phase velocity and group velocity, relation between phase velocity and group velocity. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number. In that case, the relationship between e and k will not be k 1. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. What is the difference between phase velocity and group. Jun 08, 2007 the phase and group velocities are not equal when the wave is dispersive. In an anomalous medium, the group velocity is greater than. Is there any unconventional method to find out the relation between group velocity and phase velocity. 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. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd. Group and phase velocity wolfram demonstrations project.
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