Matter Waves: Phase vs Group Velocity Equation

[rg414]

Homework Statement

In a particular substance the phase velocity of the waves is proportional to the reciprocal of the wavelength. If v_p represents the central phase velocity of a wave group and v_g represents the group velocity, which of the following equations is valid?

Homework Equations

(A) v_g = 1/v_p
(B) v_g = ½ v_p
(C) v_g = v_p
(D) v_g = 2 v_p
(E) v_g = 4 v_p

The Attempt at a Solution

I'm having a hard time finding relevant information on this question. I believe the answer is C. If anyone can help me to further understand this problem, I would appreciate the help.

 

[zzzoak]

I think that
$$v_p=\frac{w}{k}=a \frac{1}{\lambda}.$$

We get from this
$$w=a \frac{k}{\lambda}=a \frac{k^2}{2 \pi}.$$

Then
$$v_g=\frac{dw}{dk}=2a \frac{k}{2 \pi}=2a \frac{1}{\lambda}.$$

$$v_g=2 v_p.$$