Velocity of Wave Packets

1. Jan 17, 2005

Hyperreality

Wave packets has a group velocity of

$$v_{group}=\frac{d\omega}{dk}$$

and its phase velocity is

$$v_{phase}=\frac{\omega}{k}$$

Show that the group velocity and the phase velocity are related by:

$$v_{group} = v_{phase} - \lambda\frac{dv_{phase}}{d\lambda}$$

Can someone please tell me where to start on this problem?

2. Jan 17, 2005

dextercioby

All u need to know besides the rules of differentiation is
$$k=:\frac{2\pi}{\lambda}$$

Daniel.

PS.Compute the RHS of your equality and show it matches the LHS.