21. This tensor expresses the change in group velocity due to a change in crystal momentum. 22. Consequently, for that wave situation, the group velocity is 23. The phase velocity drops smoothly while the group velocity drops somewhat precipitously towards a minimum. 24. The time-varying amplitude does not propagate at the phase velocity but rather at the group velocity . 25. In general, shorter waves have an eastward group velocity and long waves a westward group velocity. 26. The energy transport velocity is the group velocity . 27. In general, shorter waves have an eastward group velocity and long waves a westward group velocity . 28. However the physically more important group velocity interval is substantially larger ( proportional to ? ). 29. The group velocity is sort of the " average " speed of the whole little pulse. 30. There are two velocities that are associated with waves, the phase velocity and the group velocity .