AC foundations
Wave speed in a medium
- where
- wave speed in the medium (m/s)
- relative permittivity
- relative permeability
Explain this equation
Estimates how fast an electromagnetic wave travels through a material rather than a vacuum. Useful for understanding signal timing in cables and why a cable's velocity factor is below one.
299792458 is the speed of light in a vacuum in m/s, the exact defined value. εr is relative permittivity: how strongly the material responds to an electric field compared with a vacuum. μr is relative permeability: the same idea for magnetic fields. Both are plain ratios with no units, and a vacuum has 1 for each.
A wave's speed depends on how readily the medium stores electric and magnetic energy. The more it stores, the slower the wave, so the vacuum speed is divided by the square root of εr × μr.
With εr = 4 and μr = 1 the speed is halved, to about 150,000 km/s. Most insulating materials are non-magnetic, so μr is usually 1 and only εr matters. Quadrupling εr halves the speed.
Watch out: this is the speed of the wave, not the drift speed of electrons, which is tiny. Real cable propagation also depends on geometry and frequency.
In the simple lossless-medium model, electrical and magnetic material properties set electromagnetic wave speed. The equivalent absolute-property formula is v = 1/√(εμ).
Relative values have no units. Do not mix relative and absolute properties in the same formula.
Enter your values to see the result.
Common mistake
Assuming this is electron drift speed.
Limits
Homogeneous, linear, lossless model; real cable propagation depends on geometry and frequency. Uses the exact vacuum light speed, 299,792,458 m/s, rather than the rounded teaching value.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.