The relation between group velocity and phase velocity are. As i understands it, when group velocity exceeds c, it is necessarily in special matter amplified crystal, and the final pulse is not the same as the initial one. 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. Difference between phase velocity and group velocity velocity. 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. 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. 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 this note is part of the supporting online material for the textbook \solid state physics. Difference between phase velocity and group velocity. It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. Relation between phase velocity and group velocity learn only in 1. 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 group velocity is defined to be the velocity at which the envelope of a wave travels. Group velocity, poynting and polarisation group velocity phase velocity is the rate of advance of constant phase surfaces.
Its true that i introduced the notsoobvious equation for group velocity, but then i proceeded to use that equation in a very mechanical way. This document is highly rated by civil engineering ce students and has been viewed 2310 times. This is the velocity at which the phase of any one frequency component of the wave travels. So, the phase velocity equals to the group velocity.
The group velocity for xrays represents the velocity of a group of waves in which each. You can nd more information on the distinction between the. A onedimensional harmonic wave figure 1 is described by the equation. Here is a simple way to think about the difference. Phase velocity and group velocity civil engineering ce. Pdf on energy flux and group velocity researchgate. Velocity with which the phase of a wave travels is called phase velocity. Pdf closedform expressions are derived for phase velocity and group velocity in cylindrical and spherical sound waves. Phase and group angles and velocities stanford university. Going back to the case of airfilled waveguide, the group velocity is. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. Isnt the derivation already available in that link.
Phase velocity and group velocity in a wave packet 2 x. For debroglie mass waves, the particle frequency is a linear function of the particle energy e, so it is typical to write the. The group velocity for xrays represents the velocity of a group of waves in which each wave has a different phase velocity v p. 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. Particle waves and group velocity university of kansas. From group or phase velocities to the general anisotropic. The group velocity is the speed of the overall shape of a modulated wave called the envelope. The phase velocity is not the velocity at which stu. The group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. This shows a wave with the group velocity and phase velocity going in different directions. 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 underlying carrier wave called the group velocity.
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. 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. 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. Group velocity and phase velocity university of british. 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. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. The table below shows phase velocity for certain rocks at various frequencies. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029.
Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. The phase velocity surface for waves propagating in a uniform cold plasma is sometimes misinterpreted as having the shape of a wavefront. 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 phase velocity, ray velocity, and group velocity surfaces for a. The relation between group velocity and phase velocity are proportionate. Apr 17, 2020 phase velocity and group velocity civil engineering ce notes edurev is made by best teachers of civil engineering ce. Phase velocity and group velocity in engineering physics 2 pdf free download. The inequality of group velocity, speed of light in vacuum, and phase velocity is then. Our technique is based on the use of a broadband pump and vector group velocity matching between the pump. We can obtain phase velocity from solving the wave equation. Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. The relation between the energy flux and group and phase velocities of surface waves in an arbitrary semiinfinite anisotropic.
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. 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. Then, to obtain the wave equation, we need to consider the maxwells equation. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. Phase velocity definition of phase velocity by merriam. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. Phase and group angles and velocities in anisotropic wave propagation the phase angles and velocities are different from the group angles and velocities.
Group and phase velocity wolfram demonstrations project. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd. Group and phase velocity in the example of water waves. Phase velocity definition is the velocity of a wave motion as determined by the product of the wavelength and frequency called also wave velocity. From group or phase velocities to the general anisotropic stiffness tensor robertw. The accuracy, robustness and computational complexity. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. What is the difference between phase velocity and group. Phase velocity and group velocity are two very important concepts in physics. They arise in quantum mechanics in the time development of the state function for the continuous case, i. Group and phase velocity engineering physics class. It can be engineered to look like the initial one, but it. The velocity at which a single frequency of a wave group or a phaseor part such as the crest or troughof a wave group travels through a medium. The group velocity of a wave is the velocity with which the overall envelope shape of the waves.
The individual wave forming the wave packet possesses an average velocity, vp called the phase velocity. You can nd more information on the distinction between the phase velocity and the group velocity of a wave is a. Phase velocity can exceed velocity of light in vacuum, c. Pdf phase velocity and group velocity in cylindrical and. Sending a square pulse as a basic communication tool is the main focus of this lecture. The groupvelocity vector determines the direction and speed of energy propagation i. This video is highly rated by civil engineering ce students and has been viewed 350 times. James brown abstract two numerical inversions were designed to calculate the 21 independent stiffnesses that define, in general, an anisotropic medium from either group or phasevelocity data. This is defined by chosen here to equal 1, where is the angular velocity and is the wave number. Wave packet comprises of a group of waves, each with slightly different velocity and wavelength. Phase velocity and group velocity, relation between phase velocity and group velocity duration.
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. Phase and group velocity are two important and related concepts in wave mechanics. The variations of phase velocity, group velocity, ray direction with phase direction in 3d space, are plotted for a numerical model of general. Im going to assume you meant to say the concept of group velocity has become more clear, because phase velocity is the obvious thing. In an anomalous medium, the group velocity is greater than. The difference between the group and phasevelocity vectors may be caused by velocity variations with either frequency 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. Wave packet, phase velocity and group free download as powerpoint presentation. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g.
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. Relation between group velocity and phase velocity at byjus. A fundamental relation between phase and group velocity. Phase velocity and group velocity in engineering physics 2. This is not true for light propagating in materials otherwise a prism wouldnt work or most other kinds of waves, such waves in water. 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. The phase velocity and group velocity are speed in terms of an expression which are directly equal to each other.
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