Here is a simple way to think about the difference. Phase and group angles and velocities in anisotropic wave propagation the phase angles and velocities are different from the group angles and velocities. A onedimensional harmonic wave figure 1 is described by the equation. Phase velocity and group velocity in engineering physics 2 pdf free download. Calculate the group velocity of a relativistic particle. Simultaneous negative phase and group velocity of light in. For quantum electron waves, the group velocity is twice the phase velocity, for water waves, its half the phase. In the top left is a group that moves at the same velocity as the individual wave that makes it. Pdf fundamental relation between phase and group velocity, and. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. 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 main difference between phase velocity and group velocity is that phase velocity is greater than the group velocity in a normal medium. This wave will be moving with a phase velocity given by vphase. Phase velocity definition of phase velocity by merriam. Difference between phase velocity and group velocity. They arise in quantum mechanics in the time development of the state function for the continuous case, i. What are phase velocity, group velocity, and signal 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. About the nonrelativistic limit of the phase velocity of. In the presence of dispersion, the second term in the denominator. The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other. Phase velocity and group velocity as a function of the total. Wave packets and group velocity when dealing with simple waves as is. The inequality of group velocity, speed of light in vacuum, and phase velocity is then.
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. Pdf we demonstrate that the ratio of group to phase velocity has a simple relationship. In this deepwater case, the phase velocity is twice the group velocity. Write each answer as a multiple of the speed of light c. The momentum carried away slows down the particle, and this result is similar with the previous one, but is obtained from different considerations fig. Going back to the case of airfilled waveguide, the group velocity is. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. This notes is meant to be a supplement and not a substitute for. About the nonrelativistic limit of the phase velocity. Assume a particle of mass m and traveling with a speed of v. Dispersion pl 2pl 3pl 4pl 2w0 w k slope wk phase velocity figure 3 there are various things to note about this. The relation between group velocity and phase velocity are proportionate. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity.
In a wave packet, the carrier wave travels with the phase velocity. The situation is very different in a medium with negative group velocity. Phase velocity and group velocity as a function of the total relativistic energy and the relativistic momentum of a particle 2. Pdf phase velocity and group velocity in cylindrical and. Usually, group velocity is not equal to phase velocity, except in empty space. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. The phase velocity of a wave is the speed at which a given phase of a. Group and phase velocity inversions for the general. 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 phase velocity of a wave is the rate at which the phase of the wave propagates in space. Weve seen that a free particle can be represented in quantum. Phase velocity and group velocity in engineering physics 2 pdf free. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. The phase velocity wave velocity of a wave is the velocity with which any given phase 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. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. 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. The idea of a group velocity distinct from a waves phase velocity was first. Velocity with which the phase of a wave travels is called phase velocity. Phase velocity definition is the velocity of a wave motion as determined by the product of the wavelength and frequency called also wave velocity. What is the difference between phase velocity and group. The phase speed is different from the group velocity. Sending a square pulse as a basic communication tool is the main focus of this lecture. Calculate the phase velocity of a relativistic particle. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number. It says that the wave height must be small compared to the wavelength. Particle waves and group velocity university of kansas. Phase velocity is the speed of the crests of the wave.
The group velocity is the speed of the constructed wave, created the group of waves. Frequency dispersion in groups of gravity waves on the surface of deep water. Pdf closedform expressions are derived for phase velocity and group velocity in cylindrical and. This is the velocity at which the phase of any one frequency component of the wave travels. In order to understand the nature of the group velocity, lets consider a race. We want to ignore rotation, friction and nonlinearity. Group and phase velocity wolfram demonstrations project. Consider a beam of particles traveling in free space in the same direction with nonrelativistic speed find their quantummechanical phase velocity. Light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. 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 velocity is less than velocity of electromagnetic waves in free space. This is the group velocity and is which can be found if you have giving 7 v. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering.
To begin, lets think about how to solve the wave equation in a dispersive system with initial condition ax,t0fx 9. Relation between phase velocity and group velocity by. The group velocity of a wave is the velocity with which the overall envelope shape of the waves. Phase and group velocity are two important and related concepts in wave mechanics. The group velocity is the speed of the overall shape of a modulated wave called the envelope. 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. 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. 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. A monochromatic wave has velocity called the phase velocity given by vp. Fundamental relation between phase and group velocity, and. Phase velocity and group velocity as a function of the angular frequency and the wave number 4. 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.
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. Basic concepts of quantum mechanics asaf peer1 september 10, 2015. The red dot overtakes two green dots when moving from the left to the ri. Phase velocity and group velocity in a wave packet physics pages.
The phase velocity is the speed at which one member of the phase group travels. Vary the group velocity away from unity, and carefully follow one of the packets as it moves across the screen, then carefully follow one of the individual crests. Rick salmon scripps institution of oceanography university. Group velocity and phase velocity of the electromagnetic waves is the same in free space. The table below shows phase velocity for certain rocks at various frequencies. 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 in engineering physics 2. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. Does a single photon particle move in the direction of the group velocity or the wave vector. This article tries to differentiate those differences in detail. This velocity is called the group velocity and is usually different from the.
Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. Relation between phase velocity and group velocity by education study. 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. It is explained and illustrated in this document, using little animations in the pdf le. Phase velocity is in opposite direction of group velocity. Phase velocity and group velocity for beginners vixra. A fundamental relation between phase and group velocity. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science.
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