What is phase velocity and how does it relate to group velocity?

In summary: According to the wiki page, this diagram:shows the phase velocity and group velocity moving in opposite directions. I think I understand what group velocity is, its the velocity of the overall wavepacket, in the diagram I can see a Gaussian wavepacket moving to the right so I'm guessing that's the group velocity.In summary, the phase velocity is the individual waves' average speed as they move along the x-axis within the wave packet.
  • #1
mycotheology
89
0
According to the wiki page, this diagram:
Wave_opposite-group-phase-velocity.gif

shows the phase velocity and group velocity moving in opposite directions. I think I understand what group velocity is, its the velocity of the overall wavepacket, in the diagram I can see a Gaussian wavepacket moving to the right so I'm guessing that's the group velocity. I can't see the phase velocity. I don't know what I'm looking for because I don't really know what phase means. I understand the concept of constructive and destructive interference and how 2 waves can be in or out of phase but I don't understand what phase means with respect to an individual wave. Does the word phase mean where the waveform is on the y axis, at a particular point on the x axis? Thats the idea I have of phase and with that in mind, I can't understand how phase can have a velocity.
 
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  • #2
mycotheology said:
According to the wiki page, this diagram:

shows the phase velocity and group velocity moving in opposite directions. I think I understand what group velocity is, its the velocity of the overall wavepacket, in the diagram I can see a Gaussian wavepacket moving to the right so I'm guessing that's the group velocity.

Correct!

I can't see the phase velocity.

The phase velocity refers to the individual waves "inside" the wave packet, which are moving to the left in your example. Actually, what you're seeing is the average phase velocity of the individual waves that combine to produce the wave packet.
 
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  • #3
I think the way to see the phase motion is to pick an individual peak and keep your finger on it.
 
  • #4
jtbell said:
The phase velocity refers to the individual waves "inside" the wave packet, which are moving to the left in your example. Actually, what you're seeing is the average phase velocity of the individual waves that combine to produce the wave packet.
So if I did a Fourier transform on the wavepacket and broke it down into its constituent sine waves, they'd be moving to the left. Still can't see it though. Are you able to see the individual waves inside the packet in that diagram?

Simon Bridge said:
I think the way to see the phase motion is to pick an individual peak and keep your finger on it.

Whats confusing me is the way each individual ripple is growing and shrinking as it moves from left to right. In other words, each peak is moving up and down the y-axis as it traverses the x axis. I thought that phase depended on the position on the y axis. If I follow an individual peak, I do see it moving from right to left though, should I just forget about the y axis?
 
  • #5
Group velocity is, essentially, the velocity by which ENERGY propagates. Energy is what effectively determines the actual AMPLITUDE of a given peak, whereas the peak itself moves with a different velocity. THAT velocity is what we call phase velocity.
 
  • #6
DocZaius said:
Ignore the up and down motion. Just identify a peak - any peak - and consider its left-right velocity. That is the phase velocity.

Ah right, that clears it up, thanks a lot.
 
  • #7
That's it :)
The phase is the angle that the phasor makes with the horizontal axis.
If the length of the phasor is constant, then that corresponds to the y-coordinate.
But if the length of the phasor is a function of time, then the same phase points may have different y-positions. All the peaks have the same phase - and they are easy to see - so...

http://en.wikipedia.org/wiki/Phasor (second diagram)
 

1. What is phase velocity?

Phase velocity is the speed at which the phase of a wave propagates in space. It refers to the velocity of a specific point on the wave's phase, rather than the velocity of the wave as a whole.

2. How is phase velocity different from group velocity?

Group velocity is the velocity at which the overall shape or envelope of a wave propagates. It takes into account the individual velocities of each component of the wave, while phase velocity only considers the velocity of a specific point on the wave's phase. In some cases, phase velocity and group velocity may be the same, but in others, they can differ significantly.

3. What factors affect the phase velocity of a wave?

The phase velocity of a wave can be affected by several factors, including the medium through which the wave is traveling, the frequency of the wave, and the properties of the wave itself (such as wavelength and amplitude). Additionally, the phase velocity can also be influenced by any external forces acting on the wave, such as gravity or electromagnetic fields.

4. How is phase velocity calculated?

The phase velocity of a wave can be calculated by dividing the wave's frequency by its wavenumber. This can be represented by the equation vp = f/λ, where vp is the phase velocity, f is the frequency, and λ is the wavelength. It is important to note that this calculation assumes the wave is traveling through a uniform medium.

5. What are some real-world applications of phase velocity?

Phase velocity has many practical applications in various fields, including telecommunications, radar and sonar technologies, and medical imaging. In telecommunications, phase velocity is used to analyze the performance of different transmission lines and to optimize signal transmission. In radar and sonar, it is used to determine the location and speed of objects. In medical imaging, phase velocity is utilized in techniques such as ultrasound and MRI to produce images of internal structures of the body.

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