The group velocity of a wave is the velocity with which the overall envelope shape of the waves. Phase velocity and group velocity superposition of light waves when we analyze the resultant of two or more simple harmonic vibrations monochrome light waves, we usually can treat it as the simple sum of the individual vibrations waves as shown below. 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 relation between group velocity and phase velocity are.
Calculate the group velocity of a relativistic particle. 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. Usually, group velocity is not equal to phase velocity, except in empty space. A fundamental relation between phase and group velocity. 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. That is, to within a phase factor of unit modulus the waveform fx,t is a function of a single variable,x. 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. A group of people, say city marathon runners, start. For the fictitious case of negligible dispersion, the group velocity is identical to the phase velocity, i. Phase velocity and group velocity in a wave packet physics pages. 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. To me, it doesnt make much sense what it means for phase velocity to exceed c. 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.
The phase velocity, ray velocity, and group velocity surfaces for a magnetoionic medium by a. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. For such a component, any given phase of the wave for example, the crest will appear to travel at the 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 v. You can nd more information on the distinction between the. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths.
Phase velocity and group velocity for beginners vixra. The red square overtakes two green circles when moving from the left to the right of the figure. 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. If we have two waves that are slightly di erent in frequency. A fundamental relation between phase and group velocity, and. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. 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. Difference between phase velocity and group velocity. The phase velocity, ray velocity, and group velocity. In its most general form, the groupvelocity vector can be written as e. Velocity and phase velocity of matter wave physics forums.
May 12, 2006 the group velocity v group can be expressed as. Simultaneous negative phase and group velocity of light in. We can obtain phase velocity from solving the wave equation. Assume a particle of mass m and traveling with a speed of v. Schuster with noting in 1904 that a negative group velocity, i. The table below shows phase velocity for certain rocks at various frequencies. In its most general form, the group velocity vector can be written as e. In the presence of dispersion, the second term in the denominator. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029.
Particle waves and group velocity university of kansas. Phase velocity and group velocity are two very important concepts in physics. In an anomalous medium, the group velocity is greater than the phase 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. This is the group velocity and is which can be found if you have giving 7 v. Difference between phase velocity and group velocity velocity. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. Light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. Then, to obtain the wave equation, we need to consider the maxwells equation. Relation between phase velocity and group velocity.
The speed of the monochromatic wave is just the phase velocity of the main wave. 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. Sep 12, 2012 v v g itex\frac\partial \omega\partial kitex, that is, group velocity equals the velocity of the particle associated with the wave or wave packet. The group velocity is what has to be considered for the code measurements, i. Relation between group velocity and phase velocity at byjus. 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. Walker department of physics, university of natal, durban, 4001, south africa received 22 june 1976 and in revised form 25 october 1976 the phase velocity surface for. Here is a simple way to think about the difference. Review of basic formulas for waves in spacetime x,t or perspacetime.
This velocity is called the group velocity and is usually different from the individual phase velocities of the waves that make up the packet. Calculate the phase velocity of a relativistic particle. Phase velocity definition of phase velocity by merriam. In this deepwater case, the phase velocity is twice the group velocity. Simultaneous negative phase and group velocity of light in a.
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. 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. What i dont understand is why phase velocity does not carry informationenergy where as group velocity does. Waves, the wave equation, and phase velocity what is a wave.
When phase velocity increases, proportionately group velocity will also increase. 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. 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. The red square moves with the phase velocity, and the green circles propagate with the group velocity. Since each amplitude envelope contains a group of internal waves, this speed is usually called the group velocity, vg. The group velocity is directly proportional to phase velocity. Unlike phase velocity, which can be obtained directly from the christoffel equation, group velocity depends on the phasevelocity function and, in some representations, on the polarization vector. Group velocity when the various frequency components of a waveform have different phase velocities, the phase velocity of the waveform is an average of these velocities the phase velocity of the carrier wave, but the waveform itself moves at a different speed than. 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 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. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. The phase velocity is not the velocity at which stu. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Phase and group velocity are two important and related concepts in wave mechanics. 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.
It is this modulation that represents the signal content. They arise in quantum mechanics in the time development of the state function for the continuous case, i. This is the velocity at which the phase of any one frequency component of the wave travels. Thus we see direct dependence of group velocity on phase velocity and viseversa.
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. As a result, the peak of a temporally long gaussian. 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 bs physics students. The phase velocity wave velocity of a wave is the velocity with which any given phase of the wave travels. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. 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. Signal velocity can be different from group velocity and doesnt necessarily have the invariant. In a wave packet, the carrier wave travels with the phase velocity. Group velocity and phase velocity university of british. Phase velocity is in opposite direction of group velocity. Phase velocity and group velocity as a function of the angular frequency and the wave number 4. Phase velocity and group velocity in a wave packet 2 x. Nov 18, 2019 phase velocity last updated november 18, 2019 frequency dispersion in groups of gravity waves on the surface of deep water.
A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. Signal velocity can be different from group velocity and doesnt necessarily have the invariant relationship group velocity has with phase velocity. Fundamental relation between phase and group velocity, and. Phase and group velocity matching for cumulative harmonic generation in lamb waves article pdf available in journal of applied physics 1099. Relation between phase velocity and group velocity learn only in 1. The idea of a group velocity distinct from a waves phase velocity was first proposed by w. You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a.
Velocity with which the phase of a wave travels is called phase velocity. The propagation of waves through dispersive media often leads to surprising or counterintuitive behavior. Sending a square pulse as a basic communication tool is the main focus of this lecture. To understand the difference between phase and group velocity of waves, consider the following analogy.
Pdf phase and group velocity matching for cumulative. I look at it as k wave number approaching 0 so wavelength goes to infinity. What is the difference between phase velocity and group. Nov 18, 2017 relation between phase velocity and group velocity learn only in 1. Group and phase velocity up to now we have just talked about the speed or velocity v of a wave. Phase velocity and group velocity this note is part of the supporting online material for the textbook \solid state physics. Phase and group velocities article pdf available in computer physics communications 207 june 2016 with 1,273 reads how we measure reads.
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. The phase velocity is given in terms of the wavelength. Oct 26, 2005 what i dont understand is why phase velocity does not carry informationenergy where as group velocity does. Rp photonics encyclopedia group velocity, light, envelope. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. Or, equivalently, in terms of the waves angular frequency. Phase velocity last updated november 18, 2019 frequency dispersion in groups of gravity waves on the surface of deep water.
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