Phase, group velocity and energy

In summary, the conversation discusses the concepts of phase and group velocity in EM waves. It is mentioned that phase velocity does not carry information or energy, while group velocity does. The idea of phase velocity exceeding the speed of light is also discussed. It is suggested that the energy of a wave is determined by its amplitude, which is why the group velocity is associated with equations for power flow and energy. A helpful discussion on this topic is provided for further understanding.
  • #1
CrusaderSean
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I'm studying EM waves right now and I don't understand phase and group velocity very well. I know the definitions of phase and group velocity from here and what they look like from http://www.csupomona.edu/~ajm/materials/animations/packets.html .
What I don't understand is why phase velocity does not carry information/energy where as group velocity does. phase velocity can exceed speed of light c because of this. To me, it doesn't make much sense what it means for phase velocity to exceed c. I look at it as k (wave number) approaching 0 so wavelength goes to infinity... But shouldn't poynting's theorem still apply for such a wave? namely a wave with phase velocity > c still carries energy. I think I'm confusing several issues here.
 
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  • #3
Essentially, the energy of a wave is dependant on the amplitude, which is why the envelope of the wave is associated with the energy of the wave rather than the rapid oscillatory component.

The group velocity thus features in equations for power flow and energy and so forth because the group velocity describes the propagation of the envelope.

Claude.
 

What is phase velocity and how is it different from group velocity?

Phase velocity is the speed at which the phase of a wave propagates through space. This means it is the speed at which a specific point on a wave (such as the peak or trough) travels. Group velocity, on the other hand, is the speed at which energy or information is transmitted through a wave. It takes into account the velocity of each individual point on the wave as well as the interaction between those points.

How are phase, group velocity and energy related?

All three of these properties are related to the behavior of waves. Phase velocity and group velocity are both measures of how waves propagate through space, while energy is the physical quantity that is transmitted by the wave. In simple terms, the phase velocity determines the speed at which the wave's shape moves, the group velocity determines the speed at which energy is transmitted, and energy is the physical manifestation of the wave itself.

What does it mean when the phase and group velocities are equal?

When the phase and group velocities are equal, it means that the wave is traveling at a constant speed without any distortion or dispersion. This is known as a non-dispersive wave. In this case, the energy and information carried by the wave will be transmitted at the same speed, and the shape of the wave will remain unchanged.

How do phase and group velocities affect the behavior of waves?

The phase and group velocities affect the behavior of waves in different ways. The phase velocity determines the wavelength and frequency of the wave, while the group velocity affects the spreading and dispersion of the wave. In some cases, the group velocity can also determine the direction of energy transfer in a wave.

Can phase and group velocities be manipulated?

Yes, phase and group velocities can be manipulated through various methods such as changing the medium through which the wave is traveling, using specialized materials or structures, or applying external forces to the wave. These manipulations can alter the properties of the wave and lead to interesting phenomena such as wave interference and dispersion.

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