Pdf on mar 2, 2015, daniel munozsantiburcio and others published awesome. The phase velocity of a wave is the rate at which the phase of the wave propagates in space. The groupvelocity vector determines the direction and speed of energy propagation i. 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 group velocity often depends on frequency we have seen that the phase velocity depends on, because n does. The angle insider the cos term in a certain phase is. This shows a wave with the group velocity and phase velocity going in different directions. A code for the calculation of phase and group velocities.
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 inside a waveguide does not exceed the speed of light that i am aware of, but phase velocity certainly does. In this deepwater case, the phase velocity is twice the group velocity. 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 group velocity of a wave is the velocity with which the overall envelope shape of the waves. Group and phase velocity wolfram demonstrations project. The solutions to the maxwells equations for transmission media such as transmission lines and waveguides, there are two velocities. The key to understanding this problem is that this velocity is the phase velocity. 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.
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 the frequency which cannot be propagated through the waveguide. Assume a particle of mass m and traveling with a speed of v. They arise in quantum mechanics in the time development of the state function for the continuous case, i. When the group velocity depends on frequency, this is known as group velocity dispersion, or gvd. When we look at waves breaking on a shore, it is obvious that the waves bring with them a lot of energy. Calculate the phase velocity of a relativistic particle. 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 definition of phase velocity by merriam. Phase velocity is the speed that a portion of a wave with constant phase. The group velocity often depends on frequency we have seen that the phase velocity depends on.
Note that in this particular case, both group and phase velocities are positive. The qualifier phase is used here, because the speed of a. A fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, massachusetts 029, usa 2center for materials science and engineering. In an anomalous medium, the group velocity is greater than. 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. This is the velocity at which the phase of any one frequency component of the wave travels. Group velocity and phase velocity light waves in the vacuum have the special property that the velocity is exactly the same for all wavelengths. The group velocity for xrays represents the velocity of a group of waves in which each wave has a different phase velocity v p. 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. A onedimensional harmonic wave figure 1 is described by the equation. What are phase velocity, group velocity, and signal. Velocity with which the phase of a wave travels is called phase velocity. Calculate the group velocity of a relativistic particle.
Apr 17, 2020 phase velocity and group velocity civil engineering ce notes edurev is made by best teachers of civil engineering ce. The phase velocity is not the velocity at which stu. Phase velocity is directly proportional to group velocity b. It is explained and illustrated in this document, using little animations in the pdf le. The relation between group velocity and phase velocity are. 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. Brillouin, wave propagation and group velocity, academic press, new york, 1960, chapter i. A code for the calculation of phase and group velocities of acoustic waves in. Product of phase velocity and group velocity is equal to square of speed of light d. The wave packet envelope is shown in magenta color in dashed lines. Here is a simple way to think about the difference. As a wave travels through a medium, its energy moves at the group velocity v g and its individual phases, or components, move at their phase velocity v p. It should not be surprising that the group velocity also depends on when the group velocity depends on frequency, this is known as group velocity dispersion, or gvd. The resulting wave packet travels with the socalled group velocity which is faster than the phase velocity in this case.
Going back to the case of airfilled waveguide, the group velocity is. Mungan, spring 2017 consider a beam of particles traveling in free space in the same direction with nonrelativistic speed find their quantummechanical phase velocity. The red dot overtakes two green dots when moving from the. A fundamental relation between phase and group velocity. Write each answer as a multiple of the speed of light c. Difference between phase velocity and group velocity velocity. The wave changes shape with distance as each frequency f, or wavelength. 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. 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. So, the phase velocity equals to the group velocity. Group and phase velocity up to now we have just talked about the speed or velocity v of a wave. 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 red dot moves with the phase velocity, and the green dots propagate with the group velocity. The difference between the group and phasevelocity vectors may be caused by velocity variations with either frequency velocity. How to calculate the phase and group velocity of a superposition of sine waves with different speed and wavelength. 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. Phase velocity definition is the velocity of a wave motion as determined by the product of the wavelength and frequency called also wave velocity. Hot network questions preferred syntax for two lines long pipe. Particle waves and group velocity university of kansas.
The relation between group velocity and phase velocity are proportionate. Here, we demonstrate the group and phase velocity phenomena as observed when two signals with different temporal and spectral frequencies wavelength are added to each other. Group velocity, poynting and polarisation group velocity phase velocity is the rate of advance of constant phase surfaces. The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to. Which one of the following statement is valid for phase velocity and group velocity. Negative radiation pressure and negative effective refractive index via dielectric birefringence pdf. Difference between phase velocity and group velocity. Relation between group velocity and phase velocity at byjus. We all know that it is not possible for em waves to propagate faster than. Lee discusses the phenomenon of dispersion in a realistic medium and the strategy to describe this kind of physics situation. Group velocity and phase velocity of the electromagnetic waves is the same in free space.
It is vital to have a solid understanding in both phase velocity and group velocity in order to excel in such fields. Thus, the phase velocity exceeds the speed of light. Phase velocity and group velocity civil engineering ce. The inequality of group velocity, speed of light in vacuum, and phase velocity is then. Oskooi,2 mihai ibanescu,3 maksim skorobogatiy,4 and steven g. Fundamental relation between phase and group velocity, and.
Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backwardwave structures poru loh,1, ardavan f. Group velocity and phase velocity university of british. The energy content in an infinite plane wave is obviously infinite, so we are more interested in finding the energy per unit area of the surface. 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. For such a component, any given phase of the wave for example, the crest will appear to travel at the phase velocity. Such a velocity only characterizes the propagation of waves that exist. So far, in discussing the dispersive effects signified by phase velocity, group velocity, group velocity dispersion, and so on, we have made an implicit assumption. It is the velocity which the electromagnetic waves changes it phase in the waveguide during propagation. This document is highly rated by civil engineering ce students and has been viewed 2310 times.
This is defined by chosen here to equal 1, where is the angular velocity and is the wave number. Sending a square pulse as a basic communication tool is the main focus of this lecture. Phase velocity can exceed velocity of light in vacuum, c. Does a single photon particle move in the direction of the group velocity or the wave vector. Frequency dispersion in groups of gravity waves on the surface of deep water. The table below shows phase velocity for certain rocks at various frequencies. Johnson1 1department of mathematics, massachusetts institute of technology, cambridge, ma 029. They play a vital role in fields such as wave mechanics, optics, quantum mechanics and even sound engineering. What is the difference between phase velocity and group.
59 1007 326 539 965 812 1181 617 1292 503 1171 96 156 949 705 764 411 36 409 106 1522 1451 479 877 1147 1327 356 738 1035 1131 1483 644 921 605 1054 620 331 631