Phase velocity greater than propagation velocity

In summary, the values that can vary to make phase velocity greater than propagation velocity are the frequency and angular frequency, as well as the wave number. This can also apply to electromagnetic waves, as seen in the reference links provided.
  • #1
morrobay
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With:
wavelength = 4 meters
frequency = 30 cycles/sec
period, T, = .033 sec/cycle
wave propagation velocity = 120 m/s
wave number ,k, = 2pi/wavelength = 1.57 radians/meter
angular frequency, w, = 2pi/T = 188.5 radians/sec
phase velocity = w/k = 120m/s
In the above propagation velocity equals phase velocity
Question: what values here would vary so that phase velocity is greater than propagation velocity ?
 
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  • #3
atyy said:
http://www.mathpages.com/home/kmath210/kmath210.htm

I have a copy of the above but that is in reference to EM waves.
Is it only in the case of electromagnetic waves where phase velocity can be greater than propagation velocity ?

If not then I would like to see a numerical answer to my original question
 

What is the difference between phase velocity and propagation velocity?

Phase velocity refers to the speed at which the phase of a wave travels, while propagation velocity refers to the speed at which the energy of a wave moves. In some cases, the phase velocity may be greater than the propagation velocity.

How is it possible for the phase velocity to be greater than the propagation velocity?

This phenomenon occurs when a wave travels through a medium with varying properties, such as a dispersive medium. In these cases, the phase velocity is determined by the wave's frequency and the medium's properties, while the propagation velocity is determined by the wave's energy and the medium's properties. If the medium causes the wave's frequency to increase, the phase velocity may be greater than the propagation velocity.

What are some examples of waves with phase velocity greater than propagation velocity?

One common example is a light wave traveling through a prism. As the light enters the prism, its frequency increases, causing the phase velocity to be greater than the propagation velocity. Other examples include sound waves traveling through a pipe with varying cross-sectional area, and ocean waves traveling through water with varying depth.

What are the implications of phase velocity being greater than propagation velocity?

This phenomenon can lead to interesting effects, such as the bending of light in a prism or the distortion of sound in a pipe. It can also be utilized in technologies like fiber optics, where signal transmission relies on the difference between phase and propagation velocities.

Can the phase velocity ever be equal to or less than the propagation velocity?

Yes, in some cases, the phase velocity can be equal to the propagation velocity. This occurs when a wave travels through a non-dispersive medium, where the frequency and energy of the wave are not affected by the medium's properties. The phase velocity can also be less than the propagation velocity in some cases, such as when the wave travels through a dissipative medium, where energy is lost as the wave propagates.

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