Phase velocity, Group velocity

In summary, the conversation discusses the physical meanings of two terms and how they relate to a Gaussian-shaped signal being sent through a medium. The question is whether the formula t=z/(group velocity) is correct for determining the maximum intensity of the signal. The conversation also mentions a helpful discussion on the topic and references the Feynman Lectures as a source of understanding.
  • #1
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Would someone be kind enough to please give physical meanings to these two terms? I have never fully understood their meaning and difference (although I know how to express them mathematically).

If, say, I have a Gaussian-shaped signal in the frequency domain that I am sending through a medium (such as a crystal) in the direction z say and I want to specify where the maximum intensity is as a function of t (it is at z=0 when t=0), am I right in saying that I would use:

t= z/(group velocity)

where the group velocity is obviously evaluated at the frequency of largest intensity.

Any help on this fairly basic matter would be much appreciated.
 
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  • #3
Thank you, I shall have a look but I actually think that I have a good enough understanding now having read a few relevant sections in the Feynman Lectures (sorry, this is what I should have done first).
 

1. What is the difference between phase velocity and group velocity?

Phase velocity is the speed at which the phase of a wave propagates through space, while group velocity is the speed at which the energy of a wave propagates. In other words, phase velocity describes how fast the peaks and troughs of a wave move, while group velocity describes how fast the overall shape of the wave moves.

2. How do phase velocity and group velocity relate to each other?

Phase velocity and group velocity are related by the dispersion relation, which describes how the frequency and wavelength of a wave are related. In general, the phase velocity is equal to the product of the frequency and wavelength, while the group velocity is equal to the derivative of the dispersion relation with respect to the wave vector.

3. Can the phase velocity be greater than the speed of light?

Yes, in certain cases, the phase velocity can exceed the speed of light. This is known as superluminal phase velocity and it occurs when the refractive index of the medium is less than 1. However, it is important to note that this does not violate the laws of relativity, as no information or energy is actually being transmitted faster than the speed of light.

4. How does the phase velocity and group velocity change in different mediums?

The phase velocity and group velocity of a wave can change when it travels through different mediums. This is because the refractive index, which determines the speed of light in a medium, can vary depending on the properties of the medium. In general, the phase velocity decreases as the refractive index increases, while the group velocity can increase or decrease depending on the specific dispersion relation.

5. How are phase velocity and group velocity used in practical applications?

Phase velocity and group velocity have many practical applications, particularly in the fields of optics and telecommunications. For example, the concept of group velocity is crucial in the design of optical fibers for transmitting information, while the phase velocity is important in understanding the behavior of electromagnetic waves in different mediums. They are also key concepts in the development of technologies such as radar, sonar, and laser systems.

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