Group and phase velocity wolfram demonstrations project. 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 in a wave packet physics pages. And we are supposed to show the group velocity is half the phase velocity. 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. 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. I have been given that the index of refraction of a media is inversely propotional to the vacuum wavelength. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. It is explained and illustrated in this document, using little animations in the pdf le.
In contrast, the nonrelativistic phase velocity and the relativistic phase velocity are not. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. In the top left is a group that moves at the same velocity as the individual wave that makes it. In an anomalous medium, the group velocity is greater than the phase velocity. Phase velocity and group velocity as a function of the angular frequency and the wave number 4. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science. The red dot overtakes two green dots when moving from the left to the ri. Rp photonics encyclopedia group velocity, light, envelope. Studies on phase and group velocities from acoustic logging article pdf available in applied geophysics 91. Group velocity and phase velocity university of british. The phase velocity is not the velocity at which stu. Waveguide group velocity, phase velocity, cut off frequency. From this you can see that when the cutoff frequency is reached, the phase velocity goes to infinity.
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. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. Write each answer as a multiple of the speed of light texctex. The red square moves with the phase velocity, and the green circles propagate with the 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. In a wave packet, the carrier wave travels with the phase velocity. 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. Phase velocity and group velocity in engineering physics 2 pdf free download. 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 and group velocity in engineering physics 2. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number.
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. A monochromatic wave has velocity called the phase velocity given by vp. The group velocity of a wave is the velocity with which the overall envelope shape of the waves. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. Phase velocity and group velocity for beginners vixra. Thus we see direct dependence of group velocity on phase velocity and viseversa. For airfilled waveguide, the phase velocity reduces further to. The group velocity is equal to the real velocity of the particle in both cases. Usually, group velocity is not equal to phase velocity, except in empty space. Quantities have been made dimensionless using the gravitational acceleration g and period t. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. Pdf on energy flux and group velocity researchgate.
This is the velocity at which the phase of any one frequency component of the wave travels. Sending a square pulse as a basic communication tool is the main focus of this lecture. Group delay is the length of a circuit or transmission line, divided by its 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. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. However, the speed at which information and energy actually propagates. 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 are phase velocity, group velocity, and signal velocity. Group velocity is the speed at which electromagnetic information travels.
A full set of computer generated plots of such surfaces are presented. Wave packet, phase velocity and group free download as powerpoint presentation. The relation between group velocity and phase velocity are proportionate. Simultaneous negative phase and group velocity of light in a. That is, the group velocity v g represents a modulation of a wave train packet, and as such, the wave packet carries information and energy and therefore must be less than the speed of light c, where. The resulting wave packet travels with the socalled group velocity which in the above case is faster than the phase velocity.
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. Velocity with which the phase of a wave travels is called phase velocity. Group velocity definition of group velocity by the free. The group velocity is the speed of the constructed wave, created the group of waves. A fundamental relation between phase and group 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. Phase velocity and group velocity in engineering physics 2 pdf free download or. T radians per unit distance radians per unit time phase velocity vp.
The relation between group velocity and particle velocity is shown below. Phase velocity of a wave the rate at which the phase of the wave propagates in space group velocity of a wave the velocity with which the overall shape of the waves amplitudes wave packet propagates through space. Relation between phase velocity and group velocity learn only in 1. Here is a simple way to think about the difference. You can also directly use the definition of group velocity, i. A summary is presented of the correct interpretations of the phase velocity, ray velocity, and group velocity surfaces. Relation between group velocity and phase velocity at byjus. Frequency dispersion in groups of gravity waves on the surface of deep water.
Phase velocity is the speed at which a point of constant phase travels as the wave propagates. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics. The wave packet envelope is shown in magenta color in dashed lines. 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. Pdf phase velocity and group velocity in cylindrical and. Phase and group velocity are two important and related concepts in wave mechanics.
What are phase velocity, group velocity, and signal. 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. Relation between group velocity and particle velocity in. 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. Hamilton in 1839, and the first full treatment was by rayleigh in his theory of sound in 1877. The nonrelativistic group velocity and the relativistic group velocity yield exactly the same result. Hence, not only is the phase velocity generally greater than c, it approaches infinity as.
About the nonrelativistic limit of the phase velocity of. Weve seen that a free particle can be represented in quantum. Simultaneous negative phase and group velocity of light in. This is the group velocity and is which can be found if you have giving 7 v. Review of basic formulas for waves in spacetime x,t or perspacetime. Phase velocity and group velocity as a function of the total relativistic energy and the relativistic momentum of a particle 2. Phase velocity last updated november 18, 2019 frequency dispersion in groups of gravity waves on the surface of deep water. Fundamental relation between phase and group velocity, and. The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to. The group velocity and the phase velocity are respectively given by the expressions 6. Phase velocity definition of phase velocity by merriam. The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other. Jan 20, 20 the resulting wave packet travels with the socalled group velocity which in the above case is faster than the phase velocity.
This velocity is called the group velocity and is usually different from the. The propagation of waves through dispersive media often leads to surprising or counterintuitive behavior. The phase and group velocity of the wave is dependent upon the refractive index, n. Nov 18, 2019 phase velocity last updated november 18, 2019 frequency dispersion in groups of gravity waves on the surface of deep water. 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. Group velocity is less than velocity of electromagnetic waves in free space. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. This is the quantity determined when one measures the. Phase velocity the resulting wave may be a perturbation that acts over a short distance, i.
Difference between phase velocity and group velocity. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. The red square overtakes two green circles when moving from the left. Does a single photon particle move in the direction of the group velocity or the wave vector. Pdf closedform expressions are derived for phase velocity and group. May 12, 2006 the propagation of waves through dispersive media often leads to surprising or counterintuitive behavior. Group velocity and phase velocity thread starter divgradcurl. The phase velocity is the speed at which one member of the phase group travels. Group velocity synonyms, group velocity pronunciation, group velocity translation, english dictionary definition of group velocity. Calculate the group velocity of a relativistic particle.
When phase velocity increases, proportionately group velocity will also increase. Pdf studies on phase and group velocities from acoustic. 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. The idea of a group velocity distinct from a waves phase velocity was first proposed by w. 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. Phase velocity is in opposite direction of group velocity. The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wavefront.
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. Pdf fundamental relation between phase and group velocity, and. A onedimensional harmonic wave figure 1 is described by the equation. 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. The ambiguity inthe definition of wave velocity often. Assume a particle of mass m and traveling with a speed of v.
We can obtain phase velocity from solving the wave equation. The group velocity is the speed of the overall shape of a modulated wave called the envelope. Group velocity and phase velocity of the electromagnetic waves is the same in free space. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Difference between phase velocity and group velocity velocity. The group velocity is directly proportional to phase velocity. 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. In this deepwater case, the phase velocity is twice the group velocity.
The table below shows phase velocity for certain rocks at various frequencies. 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 phase velocity is given in terms of the wavelength. The group velocity for xrays represents the velocity of a group of waves in which each wave has a different phase velocity v p. Particle waves and group velocity university of kansas. Then, to obtain the wave equation, we need to consider the maxwells equation. They arise in quantum mechanics in the time development of the state function for the continuous case, i. Or is the group velocity a weird result of the frequencywavevector uncertainty and superposition of. I am kind of stuck in a question relating to phase velocity and group velocity. What is the difference between phase velocity and group. The idea of a group velocity distinct from a waves phase velocity was first.