Group Velocity

v_g = \frac{d\omega}{dk}

Velocity at which the envelope of a wave packet propagates; represents energy transfer speed.

Variables

v_g

Group velocity

Speed of wave packet/energy

m/s

Angular frequency

Radians per second

rad/s

Wave number

Radians per meter

rad/m

Derivation

For dispersive media, v_g = dω/dk. For non-dispersive media, v_g = v_p.

Your notes

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Other waves formulas with the same quantities

SHM Displacement (Simple Harmonic Motion) shares Angular frequency
SHM Velocity (Simple Harmonic Motion) shares Angular frequency
SHM Acceleration (Simple Harmonic Motion) shares Angular frequency
SHM Maximum Velocity (Simple Harmonic Motion) shares Angular frequency
SHM Total Energy (Simple Harmonic Motion) shares Angular frequency

Where this formula is listed

Waves formulas, under Wave Properties, alongside Wave Equation, Period and Frequency, Wave Intensity, Intensity-Amplitude Relation and Inverse Square Law (Intensity).
In the waves list it comes after Transmission Coefficient and before Phase Velocity.
Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Group Velocity formula?

Group Velocity is written v_g = dω/dk. Velocity at which the envelope of a wave packet propagates; represents energy transfer speed. It belongs to Waves, under Wave Properties.

What are the units in v_g = dω/dk?

In SI units, v_g is group velocity, measured in m/s; ω is angular frequency, measured in rad/s; k is wave number, measured in rad/m.

How is the Group Velocity formula derived?

For dispersive media, v_g = dω/dk. For non-dispersive media, v_g = v_p. The result is v_g = dω/dk.