Table of Contents
Phase vs Group Velocity
Phase velocity describes how fast a single frequency component of a wave travels, while group velocity describes how fast the energy envelope moves. In non-dispersive media they are equal. In dispersive media like glass or plasma, different frequencies travel at different speeds, and the two velocities diverge.
For electromagnetic waves in vacuum, both velocities equal c = 299,792,458 m/s. In optical fibers, chromatic dispersion causes pulse broadening because different wavelengths travel at different group velocities, which limits data transmission rates over long distances.
Formulas
Where ω is angular frequency (rad/s) and k is the wave vector (rad/m). Group velocity v_g = dω/dk. For strings: v = √(T/μ), where T is tension and μ is linear mass density.
Wave Velocities in Common Media
| Wave | Medium | Velocity (m/s) |
|---|---|---|
| Light | Vacuum | 299,792,458 |
| Light | Water (n=1.33) | 225,407,863 |
| Sound | Air (20°C) | 343 |
| Sound | Steel | 5,960 |
| Seismic P | Granite | 5,500 |
Frequently Asked Questions
Can phase velocity exceed c?
Yes, in waveguides and anomalously dispersive media. However, group velocity -- the speed of information transfer -- cannot exceed c. No energy or information travels faster than light, consistent with special relativity.
What is the refractive index?
The refractive index n = c/v where v is phase velocity. Glass (n=1.5) slows light to 2/3 of vacuum speed. Water (n=1.33) slows it to 3/4. Higher refractive index means slower light and more bending at interfaces.
How does temperature affect sound velocity?
In air, v = 331 + 0.6T (m/s). In water, sound speed increases with temperature up to about 74 degrees C. In solids the effect is usually small.