What's The Difference Between Phase Velocity And Group Velocity?

Thread Starter

Glenn Holland

Joined Dec 26, 2014
705
This is a very basic physics question that I have never found a satisfactory answer (at least an answer that I can understand) about wave mechanics.

What is the difference between "phase velocity" and "group velocity"? Looking at a very simple wave phenomenon like ocean waves, I see a transverse displacement of the surface of the water that appears to be traveling in envelope toward the shore. It is also known that a particle floating on top of the water will move in sort of a circular path with a net displacement of zero, That is the particle will be in the same initial position after the wave has passed.

Seems the term "phase velocity" might refer to the velocity of the particle moving in simple harmonic motion as the wave passes.
 

nsaspook

Joined Aug 27, 2009
7,470


Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.

New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.

For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

https://en.wikipedia.org/wiki/Group_velocity#Superluminal_group_velocities
 

Thread Starter

Glenn Holland

Joined Dec 26, 2014
705
So the red square is the velocity that I would see a surf board moving at, But if I were looking at wave approaching the beach, what would I actually see happening with the green circles?
 
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