Group Velocities Explained
Groups velocities are all about how fast waves travel. It's not really that complicated, so don't panic. Yet.
Imagine you're throwing stones into a pond. Stop throwing the stones at the ducks, we're not interested in animal cruelty this time. It's the ripples you should be looking at.
The obvious thing to notice is that you have a group of ripples spreading out from where stone hit the water. They are moving at a particular speed. However, the waves themselves are actually moving faster because they are moving through the group.
Look at the diagram below. The ripples are travelling from left to right. If we follow the progress of the green wave then it starts off in the middle of the group and ends up at the far edge. It has travelled twice as far as the wave group.
And there you have it. The group velocity is different, in this case slower, to the speed of individual waves (the phase speed).