Answer:
ω is the angular velocity given by ω=2πf
k is the angular wave number given by – k=2πλ
t is time
x be the position
Vp phase velocity
Vg be the group velocity
The phase velocity of a wave is given by the following equation:
vp=ωk…..(eqn 1)
Rewritting the above equation, we get:
ω=kvp…..(eqn 2)
Differentiating (eqn 2) w.r.t k we obtain,
dwdk=vp+kdvpdk…..(eqn 3)
As vg=dwdk, (eqn 3) reduces to:
vg=vp+kdvpdk
The above equation signifies the relationship between the phase velocity and the group velocity.
Hope you understood the relation between group velocity and phase velocity of a progressive wave.
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