Handbook, chapter 4. The wave: frequency, length, speed
The whole book rests on one equation, and it is a schoolroom one: λ = c / f. The wavelength equals the speed of light divided by the frequency.
There is no need to memorise it separately — it is enough to remember what follows from it. And what follows from it is the size of an antenna, the names of the bands, and half the answers to «why doesn't it work».
Work it out yourself
Move the slider. At the top is one wavelength, and it is always one whatever the frequency: the only thing that changes is how many metres are in it. Below is that same length divided by four, next to a person 1.75 m tall.
At 433 MHz a quarter wave is seventeen centimetres, an antenna the length of a palm. At 1.9 MHz it is almost forty metres, and the person in the drawing shrinks to a line. This is not an exaggeration of scale, it is the answer to why a 160-metre antenna will not fit on a balcony while a 70-centimetre one screws onto a handheld.
The speed of light is not a metaphor here
A radio wave is the same electromagnetic field as visible light, only far longer. In vacuum it travels exactly 299 792 458 metres per second, and that is the constant that goes into the formula.
For calculations it is easier to remember it as 300 with megahertz: the wavelength in metres is roughly 300 divided by the frequency in megahertz. The error of that simplification is seven hundredths of a per cent, which is smaller than the precision with which you cut wire.
λ [m] = 300 / f [MHz]
At 7.1 MHz that is 42 metres, at 14.2 it is 21 metres, at 145 it is two metres and one centimetre. The last of those is where the band got its name.
Bands are named by length, not by frequency
«Two», «forty», «eighty» are not slang and not abbreviations. They are plain names: in radio a band is called by its wavelength, because that is what decides what you can do with it by hand.
Hearing «I'm working seventy centimetres», you know both the frequency and that the antenna fits in a rucksack. Hearing «on eighty», you know the person has a garden, or at least two supports forty metres apart.
| Name | Frequency | λ | Quarter wave |
|---|---|---|---|
| 160 m | 1.8–2.0 MHz | ≈160 m | ≈40 m |
| 80 m | 3.5–3.8 MHz | ≈80 m | ≈20 m |
| 40 m | 7.0–7.2 MHz | ≈42 m | ≈10 m |
| 20 m | 14.0–14.35 MHz | ≈21 m | ≈5 m |
| 2 m | 144–146 MHz | ≈2 m | ≈50 cm |
| 70 cm | 430–440 MHz | ≈70 cm | ≈17 cm |
One refinement you will need later
In a cable the wave travels more slowly than in vacuum — by about a third, depending on the dielectric. The frequency does not change, so it is the wavelength that shortens.
That is why a «quarter-wave» piece of cable is always shorter than a quarter wave in air, and why a first home-made antenna always comes out longer than it should. The quantity that describes this is the velocity factor, and it is covered in the chapter on the feeder.
The wavelength calculator gives λ, a half and a quarter for any frequency, allowing for the velocity factor.
Next — chapter 5, the bands: why by day you hear your neighbour and by night half of Europe.