Phase velocity and group velocity in engineering physics 2. What are phase velocity, group velocity, and signal velocity. Group velocity and phase velocity university of british. The group velocity is what has to be considered for the code measurements, i. The group velocity is directly proportional to 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. Calculate the group velocity of a relativistic particle. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have entered the front side of the sample. Sending a square pulse as a basic communication tool is the main focus of this lecture. In an anomalous medium, the group velocity is greater than the phase velocity. Phase and group velocity for a free particle physics forums. So you needneedthat the phase becomes stationarywith respect to k, which is the variable of integrationat k0.
Phase, group,andsignalvelocity the velocity of a wave can be defined inmanydifferent ways, partly because there many different kinds of waves, and partly because we can focus on different aspects or components of any given wave. The phase velocity wave velocity of a wave is the velocity with which any given phase of the wave travels. Frequency dispersion in groups of gravity waves on the surface of deep water. 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. 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. Usually, group velocity is not equal to phase velocity, except in empty space. Simultaneous negative phase and group velocity of light in.
It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. 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. Optical spacetime wave packets having arbitrary group. The second kind of velocity is the group velocity, which we will see is the particle velocity. Phase and group velocity matching for cumulative harmonic generation in lamb waves article pdf available in journal of applied physics 1099. The red dot overtakes two green dots when moving from the left to the ri. In a wave packet, the carrier wave travels with the phase velocity. The wave velocity we have been talking about so far is the phase velocity, which we have already encountered. Here, the authors present a method to control the spatiotemporal spectrum and allow arbitrary. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. The phase velocity c p blue line and group velocity c g red line as a function of water depth h, for surface gravity waves of constant period according to airy wave theory. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd.
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. Phase velocity and group velocity are two very important concepts in physics. Difference between phase velocity and 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. T radians per unit distance radians per unit time phase velocity vp.
Interpreting group velocity of free particle wave packet. Relation between phase and group velocity 2 notesgen. 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. 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. In its most general form, the groupvelocity vector can be written as e. You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a. Here is a simple way to think about the difference. For airfilled waveguide, the phase velocity reduces further to. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. 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. Unlike phase velocity, which can be obtained directly from the christoffel equation, group velocity depends on the phase velocity function and, in some representations, on the polarization vector. I can understand the phase velocity concept, as the velocity by which the phase is moving, but what is the concept of group velocity in this case free particle.
The momentum carried away slows down the particle, and this result is similar with the previous one, but is obtained from different considerations fig. So on the phase stops varying fast with respect to k. They arise in quantum mechanics in the time development of the state function for the continuous case, i. The relation between group velocity and phase velocity are proportionate. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics. Phase velocity and group velocity in a wave packet 2 x. So around k0, better be that the phase doesnt change quickly. 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. Phase and group velocity are two important and related concepts in wave mechanics. Pdf phase and group velocity matching for cumulative.
A onedimensional harmonic wave figure 1 is described by the equation. 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. Velocity with which the phase of a wave travels is called phase velocity. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science. Oct 24, 2006 group velocity x particle velocity c2. Simultaneous negative phase and group velocity of light in a. 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 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.
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 or. This means that both the carrier wave and the pulse envelope peak of the output pulse appear at the rear side of the sample before their input pulse counterparts have. Most people know it as the speed of energy propagation, but it is actually much more. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. Closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. What is the difference between phase velocity and group velocity. Controlling the group velocity of light in free space has been limited to small deviations so far. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation.
They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. 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. When phase velocity increases, proportionately group velocity will also increase. 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 of the total relativistic energy and the momentum of a particle. Phase velocity and group velocity as a function of the angular frequency and the wave number 4. Quantities have been made dimensionless using the gravitational acceleration g and period t. Group velocity and stationary phase approximation part 1. Waveguide group velocity, phase velocity, cut off frequency.
The inequality of group velocity, speed of light in vacuum, and phase velocity is then. Group delay is the length of a circuit or transmission line, divided by its group velocity. Review of basic formulas for waves in spacetime x,t or perspacetime. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Fundamental relation between phase and group velocity, and. Phase velocity and group velocity as a function of the total. This is the group velocity and is which can be found if you have giving 7 v. Group velocity is less than velocity of electromagnetic waves in free space.
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. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. Group velocity is the speed at which electromagnetic information 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. About the nonrelativistic limit of the phase velocity of. In a spectral region, phase and group velocity are negative simultaneously. In this deepwater case, the phase velocity is twice the group velocity. The situation is very different in a medium with negative group velocity. Relation between group velocity and phase velocity at byjus. Rp photonics encyclopedia group velocity, light, envelope.
Like discussed above, i can find that group velocity x phase velocity c2, but if i take the particle velocity as the velocity of the electron v above, then i cant get the same thing. Jun 26, 20 for the love of physics walter lewin may 16, 2011 duration. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. 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. Difference between phase velocity and group velocity velocity. This document is highly rated by civil engineering ce students and has been viewed 2310 times. A wave of any shape will travel undistorted at this velocity.
Pdf phase velocity approximations in a transversely. Phase velocity can exceed velocity of light in vacuum, c. Phase velocity and group velocity as a function of the total relativistic energy and the relativistic momentum of a particle 2. The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other. The table below shows phase velocity for certain rocks at various frequencies. Assume a particle of mass m and traveling with a speed of v. Free code to perform opo, opa, and opg calculations.
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. Secondharmonic generation, phasematching bandwidth, and. About the propagation of light in dispersive media 1. Apr 17, 2020 phase velocity and group velocity civil engineering ce notes edurev is made by best teachers of civil engineering ce. Calculate the phase velocity of a relativistic particle. The group velocity and the phase velocity are respectively given by the expressions 6. Particle waves and group velocity university of kansas. The group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. Going back to the case of airfilled waveguide, the group velocity is.
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. Thus we see direct dependence of group velocity on phase velocity and viseversa. 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. It is explained and illustrated in this document, using little animations in the pdf le. May 12, 2006 the group velocity v group can be expressed as. 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 approximations in a transversely isotropic medium article pdf available in journal of seismic exploration 2 november 2004 with 37 reads how we measure reads. From this you can see that when the cutoff frequency is reached, the phase velocity goes to infinity. A fundamental relation between phase and group velocity.
So, now we continue with the second half of the wave equation section. The ambiguity inthe definition of wave velocity often. In the presence of dispersion, the second term in the denominator. Group velocity, poynting and polarisation group velocity phase velocity is the rate of advance of constant phase surfaces. Group velocity and phase velocity san jose state university. The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n cv p ck. Group velocity and phase velocity of the electromagnetic waves is the same in free space. Phase velocity and group velocity civil engineering ce. 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. Its a bit underwhelming, but from a technical standpoint phase and group velocities are functions, with different values at different frequencies. Secondharmonic generation, phase matching bandwidth, and group velocity mismatch gvm phase matching in shg phase matching bandwidth group velocity mismatch nonlinearoptical crystals practical numbers for shg electrooptics. What is the difference between phase velocity and group. Only when the phase stops, you get a large contribution. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i.