Show by derivation that P=K÷(V_P)

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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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