Question:

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

Updated On: Oct 1, 2024
  • C[cos(kd/2)sin(kd/2)(kd/2)]C[\cos(kd/2)-\frac{\sin(kd/2)}{(kd/2)}]
  • Ccos(kd/2)C\cos(kd/2)
  • C[cos(kd/2)+sin(kd/2)(kd/2)]C[\cos(kd/2)+\frac{\sin(kd/2)}{(kd/2)}]
  • Csin(kd/2)(kd/2)C\frac{\sin(kd/2)}{(kd/2)}
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The Correct Option is B

Solution and Explanation

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