Group velocity from dispersion relation¶
Waves can form a group, called wave packets. The speed with which a wave packet travels is called group velocity. In other words, it is the speed with which the overall envelope shape of the wave’s amplitudes — called envelope of modulation of the wave — propagates through space.
Links:
- angular_wavenumber¶
angular_wavenumberof the wave.- Symbol:
k- Latex:
\(k\)
- Dimension:
angle/length
- group_velocity¶
group_speedof the wave packet.- Symbol:
v_g- Latex:
\(v_\text{g}\)
- Dimension:
velocity
- angular_frequency¶
angular_frequencyof the wave as a function ofangular_wavenumber, also called the dispersion relation of the wave.- Symbol:
w(k)- Latex:
\(\omega{\left(k \right)}\)
- Dimension:
angle/time
- law¶
v_g = Derivative(w(k), k)- Latex:
- \[v_\text{g} = \frac{d}{d k} \omega{\left(k \right)}\]