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Wave packets and group velocity
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Envelope of a combined wave moves at group velocity.
v_g = dω/dkA pulse is a superposition of many frequencies. The envelope moves at the group velocity v_g = dω/dk, while the crests travel at the phase velocity ω/k. Energy and information move at v_g.
Deep water waves: v_g is half v_p.
In dispersive media they differ.
In more detail
A wave packet is a localised group of waves with a range of frequencies. Its envelope moves at the group velocity, which can differ from the phase velocity of the individual waves.
Real-world uses
- Quantum particles are described as wave packets.
- Signals in communication systems are modulated as wave packets.
- A signal made of many frequencies, such as a radio pulse, moves at the group velocity, which is the speed of its envelope.
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Frequently asked questions
Why do packets spread?
Because their component waves travel at different speeds in dispersive media.
Is group velocity the signal speed?
Yes, in most cases the information travels at the group velocity.
Why is group velocity important?
It is the speed at which information or energy carried by a wave packet actually travels.
Related topics in Waves & Sound
Shock waves and sonic boom · Mach number · Energy transport in waves · Dispersion · Waves in water · Tsunami and shallow water waves