Phase Velocity & Group Velocity.

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Presentation transcript:

Phase Velocity & Group Velocity

Sinusoidal waves They are Progressive Wave This is standing wave

T t

x

New position of at

Phase velocity =The speed with which the constant phase moves

Group velocity

Phase velocity Group velocity

vp < vg t = 0

vp < vg t = 1

vp < vg t = 2

vp < vg t = 3

vp < vg t = 4

vp < vg t = 5

vp < vg t = 6

vp < vg t = 7

vp < vg t = 8

vp < vg t = 9

vp < vg t = 10

vp = vg t = 0

vp = vg t = 1

vp = vg t = 2

vp = vg t = 3

vp = vg t = 4

vp = vg t = 5

vp = vg t = 6

vp = vg t = 7

vp = vg t = 8

vp = vg t = 9

vp = vg t = 10

vp > vg t = 0

vp > vg t = 1

vp > vg t = 2

vp > vg t = 3

vp > vg t = 4

vp > vg t = 5

vp > vg t = 6

vp > vg t = 7

vp > vg t = 8

vp > vg t = 9

vp > vg t = 10

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

Phase and Group velocity vg P’

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

Electromagnetic waves in Ionosphere, wave guides

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

term and T term are comparable

Long waves in deep water

Short ripples under surface tension

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