Formula
Wavelength is speed divided by frequency. In vacuum the speed is the defined constant 299,792,458 m/s. A velocity factor multiplies that speed. It is the fraction of c that a wave manages inside a cable or along a loaded antenna. Sound uses an ideal-gas dry-air model, 331.3 m/s at 0°C, times the square root of the absolute temperature over 273.15.
λ = v / f
v = c × velocity factor
v_sound = 331.3 × √(1 + T/273.15)
Feet are metres divided by 0.3048. The dipole calculator takes the radio wavelength and applies an end-effect factor. Cable velocity factors for the listed coax types are on the coax loss page.
Worked examples
100 MHz in vacuum. 2.99792458 m, 9.836 ft.
The same frequency at velocity factor 0.66. 1.9786 m.
1 kHz in dry air at 20°C. Speed is 343.21 m/s. Wavelength is 0.3432 m, about 1.126 ft. 0.3432 m is the figure this page locks.
Reference
Sound at 0°C is 331.3 m/s in this model. At 20°C it is 343.21 m/s. Humidity is not included.
Questions
What is the wavelength of 100 MHz in vacuum?
2.9979 m, which is c divided by 100 MHz. c is 299,792,458 m/s.
What does a velocity factor do?
It scales the speed. A factor of 0.66, typical of solid-polyethylene coax, makes the wavelength 0.66 of the vacuum figure. It does not change the frequency.
How fast is sound at 20°C?
331.3 × √(1 + 20/273.15) = 343.2 m/s in this ideal-gas model of dry air. Humidity and wind are not in it.
Sources
- c = 299,792,458 m/s, the defined SI constant.
- Dry-air sound speed 331.3 √(1 + T/273.15) m/s, with T in °C. A planning model, not a measured atmosphere.