Question

The phase velocity vp of transverse waves on a one-dimensional crystal of atomic separation d is related to the wavevector k as
$v_p=C\frac{\sin(kd/2)}{(kd/2)}$
The group velocity of these waves is

• A. $C[\cos(kd/2)-\frac{\sin(kd/2)}{(kd/2)}]$
• B. $C\cos(kd/2)$
• C. $C[\cos(kd/2)+\frac{\sin(kd/2)}{(kd/2)}]$
• D. $C\frac{\sin(kd/2)}{(kd/2)}$

Answer 1

Answer: (B)

$C\cos(kd/2)$

Answer 2

The correct option is (B) : $C\cos(kd/2)$.