Group And Phase Velocity Pdf

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group and phase velocity pdf

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Published: 09.05.2021

A wavefront is a line or surface of constant phase. In a snapshot of a wave at one moment of time, the direction of propagation of the wave is across the wavefronts. The visual situation is different in a spacetime diagram.

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The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space. 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. The expanding ring of waves is the wave group , within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The shorter waves travel faster than the group as a whole, [ citation needed ] [ dubious — discuss ] but their amplitudes diminish as they approach the leading edge of the group. The longer waves travel more slowly, and their amplitudes diminish as they emerge from the trailing boundary of the group.

Group velocity

We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship including the case of dispersive and negative-index materials offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers. COVID has impacted many institutions and organizations around the world, disrupting the progress of research.

Difference Between Phase Velocity and Group Velocity

According to quantum physics, particles sometimes behave like waves. In some cases, waves behave like particles. This property of particles and waves is known as the wave- particle duality. This dual nature of particles and waves allow us to represent a particle in terms of waves. Based on this concept, waves are used to represent particles as it is an essential step when we deal with particles in quantum physics. However, we must add many waves, having different angular frequencies and amplitudes in particular ways, in order to get a wave packet which represents a particle. Within this concept, there are two types of velocities namely phase velocity and group velocity.

Folder Name. Folder Description. Phase velocity. Subscribe to Digital Library. Erratum Email Alerts notify you when an article has been updated or the paper is withdrawn. Visit My Account to manage your email alerts. Email or Username Forgot your username?


The distinction between the phase velocity and the group velocity of a wave is a concept of document, using little animations in the pdf file. You have to click.


Group velocity

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Wave:de-localized spread out in space and time How do we associate a wave nature to a particle? What could represent both wave and particle? Find a description of a particle which is consistent with our notion of both particles and waves Fits the wave description Localized in space A Wave Packet 3 of the group envelope is non-zero only in the neighbourhood of the particle A wave packet is localized a good representation for a particle!

Douglas C. Nyman, Harsh K. Gupta, Mark Landisman; The relationship between group velocity and phase velocity for finite, discrete observations. Bulletin of the Seismological Society of America ;; 67 5 : — For observations of both group velocity and phase velocity, the requirement that they be mutually consistent can reduce observational errors.

Group velocity

The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space. 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. The expanding ring of waves is the wave group , within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The shorter waves travel faster than the group as a whole, [ citation needed ] [ dubious — discuss ] but their amplitudes diminish as they approach the leading edge of the group.

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