1. Phase Velocity
&
Group Velocity

2. Sinusoidal waves
They are Progressive Wave
This is standing wave

3. T t

4. x

5. New position of at

6. Phase velocity =The speed with which the
constant phase moves

7. Group velocity

8. Phase velocity
Group velocity

10. vp < vg
t = 0

11. vp < vg
t = 1

12. vp < vg
t = 2

13. vp < vg
t = 3

14. vp < vg
t = 4

15. vp < vg
t = 5

16. vp < vg
t = 6

17. vp < vg
t = 7

18. vp < vg
t = 8

19. vp < vg
t = 9

20. vp < vg
t = 10

21. vp = vg
t = 0

22. vp = vg
t = 1

23. vp = vg
t = 2

24. vp = vg
t = 3

25. vp = vg
t = 4

26. vp = vg
t = 5

27. vp = vg
t = 6

28. vp = vg
t = 7

29. vp = vg
t = 8

30. vp = vg
t = 9

31. vp = vg
t = 10

32. vp > vg
t = 0

33. vp > vg
t = 1

34. vp > vg
t = 2

35. vp > vg
t = 3

36. vp > vg
t = 4

37. vp > vg
t = 5

38. vp > vg
t = 6

39. vp > vg
t = 7

40. vp > vg
t = 8

41. vp > vg
t = 9

42. vp > vg
t = 10

43. t2 t0 t1 Non dispersive: All colours moving with same speed
Dispersive: Red moving faster than blue

44. Phase and Group velocityvg P’

45. vp = Constant Non dispersive waves
Signal is propagated without distortion
More generally vp is a function of
(or k)

46. Electromagnetic waves
in Ionosphere, wave guides

47. Water waves
= density
= surface tension
h = depth of water

48. term and T term are comparable

49. Long waves in deep water

50. Short ripples under surface tension

51. Long waves in Shallow water
[ ]kh
Vg ≈ Vp
Tsunami