Sound and Wave - Group Velocity

The dispersion law for a certain type of wave motion is ω = (c²k²+m²)^½, where ω is the angular frequency, k is the magnitude of the propagation vector, c and m are constants. The group velocity of these waves approaches 

A. Infinity as k → 0 and zero as k → ∞
B. Infinity as k → 0 and c as k → ∞
C. c as k → 0 and zero as k → ∞
D. Zero as k → 0 and infinity as k → ∞
E. Zero as k → 0 and c as k → ∞

(GR8677 #59)

Solution:





As k → 0, v_g = 0
As k → ∞, v_g = c
since m ≪ →

Answer: E