Group Velocity and Phase Velocity
Group Velocity and
Phase Velocity
Tuesday, 10/31/2006 Physics 158
Peter Beyersdorf
Document info
14. 1
Class Outline
Meanings of wave velocity Group Velocity Phase Velocity
Fourier Analysis Spectral density Power Spectrum
Spectral measurements
14. 2
Phase Velocity
For a sinusoidal wave, or a waveform comprised of many sinusoidal components that all propagate at the same velocity, the waveform will move at the phase velocity of the sinusoidal components We've seen already that the phase velocity is
vp=/k What happens if the different components of the wave have different phase velocities (i.e. because of dispersion)?
14. 3
Phase and Group Velocity
No dispersion (vp=vg)
E1 E2 E1+E2
Dispersion (vpvg)
E1 E2 E1+E2
14. 4
Group Velocity
When the various frequency components of a waveform have different phase velocities, the phase velocity of the waveform is an average of these velocities (the phase velocity of the carrier wave), but the waveform itself moves at a different speed than the underlying carrier wave called the group velocity.
14. 5
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