Wavelength and frequency
| Wavelength and frequency | |
|---|---|
| Frequency | Number of complete cycles per second, measured in hertz (Hz) |
| Wavelength | Distance a wave travels during one cycle |
| Speed of radio waves | About 300,000 km per second in free space, the speed of light |
| Key formula | wavelength (m) = 300 / frequency (MHz) |
| Handy formulas | |
| Half-wave dipole | 468 / frequency (MHz), in feet |
| Quarter-wave vertical | 234 / frequency (MHz), in feet |
| Inside a feed line | Multiply the wavelength by the line's velocity factor |
Wavelength and frequency are two ways of describing the same radio wave. Frequency is how many times each second the wave goes through a complete cycle; wavelength is the distance the wave travels during one cycle. Because radio waves in free space all travel at the speed of light, the two are locked together: when the frequency goes up, the wavelength gets shorter in exact proportion. Hams use both all the time, which is why the band at 14 MHz is called the 20-meter band.
Units
Frequency is measured in hertz (Hz), one cycle per second, named after the German physicist Heinrich Hertz. Radio frequencies are large numbers, so they are usually given in kilohertz (kHz, thousands of hertz), megahertz (MHz, millions) or gigahertz (GHz, billions). The same frequency can be written several ways: 7,074 kHz and 7.074 MHz are identical. Wavelength is measured in meters, or in centimeters on the higher bands.
The formula
Radio waves travel at about 300,000,000 meters per second (more precisely 299,792,458). Dividing that speed by the frequency gives the wavelength, and with frequency in megahertz the arithmetic becomes simple:
- wavelength (m) = 300 / frequency (MHz)
- frequency (MHz) = 300 / wavelength (m)
Some worked examples:
- 14.2 MHz: 300 / 14.2 = 21.1 meters
- 146.52 MHz: 300 / 146.52 = 2.05 meters, in the 2-meter band
- 446 MHz: 300 / 446 = 0.67 meters, or 67 centimeters, in the 70-centimeter band
- Working backward, a wavelength of 6 meters is 300 / 6 = 50 MHz, the bottom of the 6-meter band
For wavelength in feet, use 984 / frequency (MHz). The 300 formula is a staple of the Technician exam.
Band names
Amateur bands are usually named by their approximate wavelength. The names are rounded, so the 40-meter band is really closer to 42 meters, and a few names are only loose approximations.
| Band | US frequencies | Wavelength at mid-band |
|---|---|---|
| 160 meters | 1.8–2.0 MHz | About 158 m |
| 80 meters | 3.5–4.0 MHz | About 80 m |
| 40 meters | 7.0–7.3 MHz | About 42 m |
| 20 meters | 14.0–14.35 MHz | About 21 m |
| 10 meters | 28.0–29.7 MHz | About 10.4 m |
| 6 meters | 50–54 MHz | About 5.8 m |
| 2 meters | 144–148 MHz | About 2.05 m |
| 70 centimeters | 420–450 MHz | About 69 cm |
Wider ranges of the spectrum have names too. HF (high frequency) runs from 3 to 30 MHz, wavelengths of 100 down to 10 meters. VHF (very high frequency) is 30 to 300 MHz, 10 meters down to 1 meter, and UHF (ultra high frequency) is 300 MHz to 3 GHz, 1 meter down to 10 centimeters. The 160-meter band technically lies just below HF, in the medium-frequency range, but hams usually group it with the HF bands.
Antenna lengths
Antenna size follows wavelength, which is why HF antennas are measured in tens of feet and UHF antennas in inches. A half wavelength in free space is 492 / frequency (MHz) feet, but a practical wire dipole comes out about 5 percent shorter because of effects at the ends of the wire. The standard starting formula is:
- Half-wave dipole length (feet) = 468 / frequency (MHz)
For 7.1 MHz that gives 468 / 7.1 = 65.9 feet, about 33 feet per side. For 28.4 MHz it gives 16.5 feet. The metric version is 143 / frequency (MHz) in meters.
A quarter-wave vertical or whip is half that length: 234 / frequency (MHz) feet. At 146 MHz that is 1.6 feet, about 19 inches. These formulas give a starting point; the final length is found by trimming while checking the SWR.
Velocity factor
Radio waves travel more slowly through a cable than through free space, because the insulation between the conductors slows them down. The ratio of the two speeds is the line's velocity factor, about 0.66 for solid-insulation coax and 0.8 or more for foam types. Inside a feed line, one wavelength is the free-space wavelength multiplied by the velocity factor.
For example, a quarter-wave section of solid-insulation coax for 146 MHz is not 300 / 146 / 4 = 0.51 meters long but 0.51 × 0.66 = 0.34 meters, about 13 inches. Velocity factor matters when a piece of line must be a specific electrical length, as in matching sections, stubs and phasing lines. For an ordinary run from the radio to the antenna, it does not.