Different expressions for group velocity

[bon]

Homework Statement

Ok so we have different expressions for group velocity, g...

The most obvious being g = dw/dk

But then the text I am using says sinve w=vk we can write

g = v+k dv/dk

alongside other expressions, including k etc..

My question is - what is v in the equation above? I thought there were only two characteristic velocities of a wave packet which is the superposition of many different waves - the group and phase velocities.. What is the physical meaning of v here..

Thanks

 

[gabbagabbahey]

Compare the equation $\omega=vk$ to the definition of phase velocity and you will see