The Electromagnetic Spectrum

Every band you will ever be allowed to use has two names: a frequency, which is what the dial shows, and a wavelength, which is what amateurs actually say out loud. Nobody calls 14.2 MHz “the fourteen megahertz band”; it is twenty metres. Converting between the two in your head, and knowing which ITU band a given frequency falls in, is worth several marks in Section A and is the arithmetic you will use every time you read a band plan for the rest of your life.

What a radio wave is

An electromagnetic wave is not one thing but two, locked together. A changing electric field creates a magnetic field; that changing magnetic field creates an electric field; and the pair regenerate each other endlessly as they travel. Neither can exist without the other.

The geometry is examined, so learn it precisely: the electric field and the magnetic field are at right angles to each other, and both are at right angles to the direction of travel. A wave in which all three directions are mutually perpendicular like this is called a transverse wave. The plane of the electric field is what defines the wave's polarisation — electric field vertical means a vertically polarised wave, which is what a vertical antenna radiates.

Velocity, and why it never changes

Radio waves are electromagnetic energy, and so is light. They travel at the same speed, and in free space that speed is a constant of nature:

Two things follow that the examiner asks directly. First, this is the same as the velocity of light — because a radio wave and a light wave differ only in frequency. Second, the velocity in free space is independent of frequency. Raise the frequency and the wave does not speed up; the wavelength shortens instead. Anything that claims velocity rises or falls with frequency is wrong on sight.

c = fλ, and the shortcut you will actually use

A wavelength is the distance a wave travels during one complete cycle. If the wave travels c metres each second and completes f cycles in that second, then each cycle occupies c ÷ f metres:

In that form the numbers are unwieldy. Put frequency in megahertz, which is how every radio is labelled, and the powers of ten collapse:

λ = (3 × 10⁸) ÷ (f × 10⁶) = (3 × 10⁸ ÷ 10⁶) ÷ f = 300 ÷ f

Note that the 300 is not a magic number: it is 3 × 10⁸ divided by 10⁶, and it only works when frequency is in megahertz and wavelength in metres. If you are given kilohertz, use λ = 300 000 ÷ f (kHz), or convert to MHz first, which is safer.

Doing it in your head

• The product is always 300. Frequency in MHz times wavelength in metres equals 300, whichever way you are working. If your two numbers do not multiply to about 300, you have divided the wrong way round.
• Double the frequency, halve the wavelength. 150 MHz is 2 m, so 300 MHz is 1 m and 75 MHz is 4 m.
• Anchor three points. 3 MHz = 100 m, 30 MHz = 10 m, 300 MHz = 1 m. Everything in between can be estimated from those.
• Band names are rounded, not exact. 7.05 MHz is really 42.6 metres but the band is called 40 m; 14.2 MHz is 21.1 metres and is called 20 m. Expect the exam to ask for the calculated figure, not the band name.

Try it, then check yourself

Type a frequency into the box below and the wavelength appears with the working shown, along with the ITU band it lands in and the Indian amateur allocation, if any. Work the three examples underneath by hand first, then use the tool to confirm.

Worked example 1 — frequency to wavelength

What is the wavelength of a signal on 15 MHz?

λ = 300 ÷ 15 = 20 metres

Check: 15 × 20 = 300. Correct. A tempting wrong answer is 45 m, which comes from multiplying 15 by 3 instead of dividing 300 by 15.

Worked example 2 — wavelength to frequency

What frequency corresponds to a wavelength of 2 metres?

f = 300 ÷ 2 = 150 MHz

The Indian 2 m allocation is 144–146 MHz, whose true wavelength is 300 ÷ 145 = 2.07 m. Close enough for the band to be named after it.

Worked example 3 — starting from kilohertz

The bottom of the Indian 160 m band is 1800 kHz. What is its wavelength?

Convert: 1800 kHz = 1.8 MHz. Then λ = 300 ÷ 1.8 = 166.7 metres.

So the “160 metre” band is really nearer 167 metres — and, at 1.8 MHz, it is not in the HF band at all. It is in MF, which the table below explains.

The ITU band table

The Radio Regulations divide the spectrum into numbered bands, each one a decade wide, each with a symbol and a metric name. This table is examined directly and is worth learning as a block.

The metric names are not decoration — they are the wavelengths, worked out with the formula you have just learned. HF runs 3 to 30 MHz, which by λ = 300 ÷ f is 100 metres down to 10 metres: tens of metres, hence decametric. VHF is 30 to 300 MHz, or 10 m down to 1 m: single metres, hence metric. UHF is 1 m down to 0.1 m: tenths of a metre, hence decimetric. Work the name out rather than memorising it and you cannot be caught by a distractor.

The ITU table proper begins at band 4. Band 12, 300 to 3000 GHz — decimillimetric waves — is listed but carries no symbol in the Radio Regulations.

The rule that generates the table

You do not have to remember eight ranges. One rule produces all of them:

Band 7: from 0.3 × 10⁷ = 3 000 000 Hz to 3 × 10⁷ = 30 000 000 Hz. That is 3 to 30 MHz, which is HF. The rule also tells you that each band is a decade — a factor of ten — wide, and that the upper limit of one band is the lower limit of the next.

Which raises the obvious question, and the ITU answers it explicitly: the lower limit is excluded and the upper limit is included. So HF means above 3 MHz up to and including 30 MHz. A signal exactly on 30 MHz is the top of HF, not the bottom of VHF. A signal exactly on 300 MHz is the top of VHF, not the bottom of UHF. In an exam that offers you both, that single sentence decides the mark.

How frequencies are written in the Radio Regulations

The Regulations also fix the unit a frequency must be expressed in, which is why official tables look inconsistent until you know the rule:

That rule is why the band table above stops at “3000 kHz” instead of saying 3 MHz, and at “3000 MHz” instead of 3 GHz. Working tables often bend it — WPC's Indian allocation table lists 20 m as 14000–14350 kHz where the Regulations would write 14–14.35 MHz — but it is the Regulations' rule that the paper tests.

Where the Indian amateur bands sit

Notice the trap in the first row. Amateurs habitually say “the HF bands” meaning everything below 30 MHz, but 160 m at 1.8 MHz is below 3 MHz and is therefore medium frequency, in the same ITU band as the AM broadcast stations you hear on a domestic receiver. Every other Indian HF allocation, from 80 m at 3500 kHz to the top of 10 m at 29.7 MHz, really is inside HF. The full allocation table, with power limits, is in the bands and power lesson, and the band plan tool shows it as segments you can scroll.

Beyond the radio spectrum

Radio occupies only the low-frequency end of a continuum. Keep going up in frequency — down in wavelength — and past about 300 GHz the waves are called infrared, felt as radiant heat; above that comes the narrow octave of visible light, red at the long-wavelength end and violet at the short; then ultraviolet, then X-rays and gamma rays. All of it is the same phenomenon, all of it travels at 3 × 10⁸ m/s in free space, and all of it obeys c = fλ. The only thing that changes is the frequency, and with it what the wave does when it meets matter — which is exactly why the ionosphere treats 7 MHz and 144 MHz so differently, as the propagation lesson shows.