You emit something at point a, measure it after time t at point b, and calculate the group velocity as bat. They arise in quantum mechanics in the time development of the state function for the continuous case, i. 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. The group velocity is the speed of the overall shape of a modulated wave called the envelope.
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. Group, velocity, phase velocity and dispersion in a wave packet. Closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. 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. The wave packet envelope is shown in magenta color in dashed lines. Lets continue using the superposed wave equation from above. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. When a wave moves in groups, the speed or velocity at which it moves is known as the group velocity. The phase velocity is given in terms of the wavelength.
In an anomalous medium, the group velocity is greater than the phase velocity. Phase and group velocity matching for cumulative harmonic generation in lamb waves article pdf available in journal of applied physics 1099. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Calculate the phase velocity of a relativistic particle. In this chapter, you are dealing with phase and group velocity, which are properties of waves. Group velocity and phase velocity of the electromagnetic waves is the same in free space. In the top left is a group that moves at the same velocity as the individual wave that makes it. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i. 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.
Phase velocity and group velocity for beginners vixra. As an example, if you send a pulsed carrier thru a network, the group velocity can be derived from the time delay or difference between the input rise time to the output rise time and the distance traveled. You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a. 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. Phase velocity and group velocity, relation between phase velocity and group velocity duration. Calculate the group velocity of a relativistic particle. The speed of the monochromatic wave is just the phase velocity of the main wave. Next, the term group index is a combination of the word group suggesting the relation with group velocity and the word index suggesting its analogous mathematical form to refractive index. The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. 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.
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. This test is rated positive by 94% students preparing for electrical engineering ee. Nov 18, 2017 relation between phase velocity and group velocity learn only in 1. The relation between group velocity and phase velocity are proportionate. The phase velocity is the speed at which one member of the phase group travels. Picture a very narrow and very tall triangle which has a very small base but a huge height whose direction of travel is parall. The velocity of carrier wave is called the phase velocity. What is the difference between phase velocity and group. These are plotted and compared for orders 0, 1 and 2, but the expressions are. 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. This is the velocity of the whole wavepacket, known as the group ve locity. The group velocity is the speed of the constructed wave, created the group of waves. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. 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.
However, in the case of a superposed wave, we need to carefully define its propagation velocity. In the presence of dispersion, the second term in the denominator. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. Phase velocity and group velocity in engineering physics 2. The idea of a group velocity distinct from a waves phase velocity was first proposed by w. Pdf phase and group velocity matching for cumulative. Difference between phase velocity and group velocity. Rp photonics encyclopedia group velocity, light, envelope. Fundamental relation between phase and group velocity, and.
Group velocity and phase velocity thread starter divgradcurl. This velocity is called the group velocity and is usually different from the individual phase velocities of the waves that make up the packet. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. Sep 12, 2012 group velocity is similar to the classical velocity the speed of particles and signals this is an approximation, but i dont want to go into details. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. 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, relation between phase. Phase velocity definition of phase velocity by merriam. Difference between phase velocity and group velocity 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.
Light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. We can obtain phase velocity from solving the wave equation. 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. If you want phase velocity and group velocity tests. You can nd more information on the distinction between the phase velocity and the group velocity. Velocity indicates the rate of change of the objects position r. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics.
The group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. Signal velocity can be different from group velocity and doesnt necessarily have the invariant relationship group velocity has with phase velocity. Measurements of group velocity are derived from phase velocity dispersion curves and modeled with global laterallyvarying isotropic structure. 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 phase velocity, ray velocity, and group velocity. Pdf closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. Relation between phase velocity and group velocity learn only in 1. Phase velocity definition of phase velocity by merriamwebster.
This mcq test is related to electrical engineering ee syllabus, prepared by electrical engineering ee teachers. Since in the presence of anisotropy the wavefront is not spherical, the group and phase velocity vectors generally are different. To see why the group velocity need not correspond to the speed of information in a wave, notice that in general, by superimposing simple waves with different frequencies and wavelengths, we can easily produce a waveform with a group velocity that is arbitrarily great, even though the propagation speeds of the constituent waves are all low. Oct 26, 2005 what i dont understand is why phase velocity does not carry informationenergy where as group velocity does. The group velocity is positive, while the phase velocity is negative.
Waveguide group velocity, phase velocity, cut off frequency. Simultaneous negative phase and group velocity of light in. Group velocity group delay is the length of a circuit or transmission line, divided by its group velocity. Usually, group velocity is not equal to phase velocity, except in empty space. The velocity of the envelope function given by equation 14 is v g. Sending a square pulse as a basic communication tool is the main focus of this lecture.
Relation between group velocity and phase velocity at byjus. Pdf fundamental relation between phase and group velocity, and. Phase velocity definition is the velocity of a wave motion as determined by the product of the wavelength and frequency called also wave velocity. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. A full set of computer generated plots of such surfaces are presented. 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. The tangent red line is the phase velocity and the green dashed line is the group velocity. This is the velocity at which the phase of any one frequency component of the wave travels. Phase velocity and group velocity in engineering physics 2 pdf free download or. 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. Furthermore, you should also be able to differentiate and establish the relation between phase and group velocity in physics. Rarely, some people use the terms group index of refraction or group refractive index as a synonym of group index. Fundamental relation between phase and group velocity. Pdf we demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field.
Global models of surface wave group velocity springerlink. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. A summary is presented of the correct interpretations of the phase velocity, ray velocity, and group velocity surfaces. However, a sinusoidal plane wave cannot be used to transmit information because it has infinite extent and it looks the same. The propagation velocity of an actual signal or the group velocity is always less than the speed of light in vacuum. 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 is the group velocity and is which can be found if you have giving 7 v. Relation between phase velocity and group velocity. If we have two waves that are slightly di erent in frequency. The group velocity is how fast the wave travels, but he phase velocity is just how fast the wave rises and falls.
What are phase velocity, group velocity, and signal velocity. Group and phase velocity in the spacetime x,t domain. Group and phase velocity wolfram demonstrations project. The group velocity is usually the more important physical velocity, since it determines how fast the energy in the wave packet propagates, or in quantum mechanics, how quickly the expectation value for the position of a particle moves.
Group velocity is less than velocity of electromagnetic waves in free space. Pdf phase velocity and group velocity in cylindrical and. Maps for both love and rayleigh waves are created in the period range 35 s to 175 s. Phase velocity and group velocity in a wave packet 2 x. For quantum electron waves, the group velocity is twice the phase velocity, for water waves, its half the phase velocity. Phase velocity and group velocity are two very important concepts in physics. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. Phase and group velocity 12 questions mcq test has questions of electrical engineering ee preparation. 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. Here is a simple way to think about the difference. The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other.
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. A onedimensional harmonic wave figure 1 is described by the equation. 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. The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wavefront.
Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. Assume a particle of mass m and traveling with a speed of v. Velocity with which the phase of a wave travels is called phase velocity. The phase and group velocity of the wave is dependent upon the refractive index, n. 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. In a normal medium, the phase velocity is greater than the group velocity.
In class we discussed that the velocity of a sinusoidal plane wave is u. The phase velocity is not the velocity at which stu. A fundamental relation between phase and group velocity, and. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. The velocity of component waves of a wave packet is called the phase velocity of those waves. 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. Velocity and phase velocity of matter wave physics forums.
What is the difference between phase velocity and group velocity. The group velocity is what has to be considered for the code measurements, i. This velocity is called the group velocity, since its the velocity of the envelope of a group in this case, 2 of waves traveling together. Group velocity and phase velocity university of british. 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 the. The table below shows phase velocity for certain rocks at various frequencies. The group velocity of a wave is the velocity with which the overall envelope shape of the waves. The superposed wave has two propagation velocities. Then, to obtain the wave equation, we need to consider the maxwells equation. You can download free phase velocity and group velocity pdf from edurev by using search above. Clearly the velocity of a monochrome light equals its equiphase surface propagation velocity. Feb 16, 2019 here is a simple way to think about the difference.
Particle waves and group velocity university of kansas. Group velocity let us consider the einsteins total. Phase velocity and group velocity as a function of the total. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd. Phase velocity vs group velocity group velocity is applicable when there is information or modulation added to a carrier frequency. 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. Review of basic formulas for waves in spacetime x,t or perspacetime. Phase velocity and group velocity civil engineering ce. The data set of group velocity measurements includes over 50,000 minorarc observations and 5,000 majorarc observations. You can also find phase velocity and group velocity ppt and other civil engineering ce slides as well. Although we arent smart enough to bore you with the details of how this is derived order a copy of pozar from our book page, group velocity is slowed by the inverse of the factor that phase velocity is increased. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number.
To me, it doesnt make much sense what it means for phase velocity to exceed c. Phase velocity and group velocity in a wave packet physics pages. Phase and group velocity are two important and related concepts in wave mechanics. This notes is meant to be a supplement and not a substitute for.
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