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Amateur Radio Info & Exams - Frequency & Wavelength

Frequency & Wavelengths

An important parameter when describing radio signals is their frequency, shown with an f, often in italics. This is the number of oscillations per second, measured in Hertz (Hz). Practical radio signals are in the kilohertz (kHz), Megahertz (MHz), or Gigahertz (GHz).

In space these signals travel at the speed of light (c), and very slightly slower in air. The speed of light is 299 792 458 metres / second. In antenna wire, and different feed-lines the speed varies greatly, from around 95% down to 66%.

Wavelength is how far a wave travels while completing a full cycle, and is represented with the lower case Greek character, lambda, λ. It is typically expressed in metres, centimetres, or millimetres. Bands are often named for the approximate wavelength in metres or cm. Millimetre waves are at the upper end of the microwave band, hundreds of Gigahertz.

Wavelength can be calculated if we know the frequency and the speed (velocity, v) of the wave in the medium:

λ = v / f
f = v / λ

Suppose a station was operating at 10 MHz. What is its wavelength? (Pro-tip: rounding to 300,000,000 is common.)

λ = 300 000 000 / 10 000 000 - so many zeros! Thankfully, we can get rid of (cancel out) a bunch of zeros, getting 300/10, and that is a popular shortcut, 300 divided by the frequency in Megahertz (MHz). As you will notice, a y = constant / x calculation can be swapped to x = constant / y. Anyway, our answer is 30 metres, the name of this band. (Note that on this band, only CW and data are allowed, with Australia one of the only places voice is allowed.) If you heard someone talking about "11 metres" you could do 300 / 11 = 27.2727, realise they were talking about 27 MHz or "HF" CB, in spectrum which was once a Ham band in some countries.

You can also use this formula to work out how long an antenna must be for a particular band or frequency. Popular examples are the quarter-wave vertical, mounted on vehicles, either by punching a hole in the roof, or using a large magnetic base, various gutter or boot-lid grips, or a bullbar mount. 5/8 are also popular. Another is the half-wave dipole, consisting of two quarter-wave wires, one each side of the feed-point, and usually hung horizontally between two trees, poles, etc. If high they radiate signals off broadside to the antenna. Mounted low, they have a more omni-directional pattern.

A quarter-wave antenna for 146 MHz is how long? If we use MHz, λ = 300 / f = 300 / 146 = 2.055 metres. Divide that by 4, and you get a fraction over 50 cm. But despite the Metric Act 1975, the tests use archaic British units in places. There are 2.54 centimetres in one inch, so 50 / 2.54 = 19.68 of these units. Practical antennas are often marginally shorter than this - about 5% shorter, or 95% of the calculated length, in this case just over 19". Beyond the scope of the test, the full calculation is: Length = 299792458 / 146 x 0.25 x 0.95 / 1000 / 25.4 = 19.19984596". Unless you are driving in deep gorges, or have to worry about low car-parks, a 5/8 wavelength antenna concentrates the energy towards the horizon, for better range.

What about a half-wave dipole for 6 metres? Why, 3 metres! But 300 / 2.54 = 118 inches. Multiply it by 0.95 and we get close to 112 inches, the answer they want. By the way 300 / 6 gets us 50 MHz. This band runs from 50 to 54 MHz, with the part up to 50.1 MHz a Morse only section or "sub-band" in the US.

Many people make the antenna slightly over-length, then trim it using a standing wave meter (SWR meter), a directional power meter, or an antenna analyser, the first two options requiring a transmitter, the last containing its own oscillator.

The radio spectrum is officially divided into bands, with the ones more relevant to Amateur Radio below. The abbreviations and frequency ranges are as per the ITU system. The wavelengths are explanatory.

VLF3 to 30 kHz100 to 10 km
LF30 to 300 kHz10 to 1 km
MF300 to 3000 kHz1000 to 100 m
HF 3 to 30 MHz100 to 10 m
VHF30 to 300 MHz10 to 1 m
UHF300 to 3000 MHz100 to 10 cm
SHF3 to 30 GHz10 to 1 cm
EHF30 to 300 GHz10 to 1 mm

Note that there is no sudden change in the characteristic of the signal propagation as you, say, go from 2999 kHz to 3001 kHz, or from 29.999 MHz to 30.001 MHz. The lowest frequency shortwave band is around 2.3 MHz, technically mediumwave.

Higher powered longwave (low and very low frequency) stations can provide continent wide signals, and are used for both broadcasting (in Europe) and time-signals (in Europe and North America). Mediumwave signals, both broadcast band and 160 metres typically has local coverage during the day, becoming state-wide or Trans-Tasman at night. Shortwave or high-frequency bands provide local, regional and global coverage, depending on the time of day, time of year, band selected, and antenna configuration. VHF and UHF bands provide local and line-of-sight communications under normal conditions, with the microwave (SHF) end being purely line-of-sight, unless you can bounce the signals off something, such as a rain storm, or a metallic surface.

27 MHz, used for CB, and inshore boating in Australia; and 10 metres (28-29.7 HMz) are often VHF-like in its local coverage. However, when the ionosphere changes, especially in summer, suddenly these bands; six metres; and even 70 MHz, the European 4 metre band; all become DX (long distance) bands. NZ CB was placed at 26 MHz, apparently to preserve Trans-Tasman telephone call revenue, although they Kiwis can also use Australian channels now that calls are affordable, and there are also Internet (VoIP) options.

Long distance propagation on VHF and UHF bands tends to be via tropospheric phenomena, such as "ducts" between temperature inversions in the atmosphere, or is related to East Coast high pressure systems, which tend to cause clear weather during summer. Otherwise signals can be bounced off the moon, using high gain antennas, off ionised meteor trails, or either the fuselages of aircraft or their condensation trails.

These ducts can also propagate TV, broadcast FM, and VHF marine signals, with one example being the volunteer marine radio base operators at Nelson's Bay, near Newcastle complaining of hearing signals from Ceduna, South Australia, during summer.

VHF & UHF Bands

The following are the US VHF and UHF bands, all of which are available to Technicians. Some are included in the exam.

6 m50 to 54 MHz50-50.1 CW only
2 m144 to 148 MHz144-144.1 CW only
1.25m219 to 220 MHzPacket Forwarding ONLY
1.25m222 to 225 MHz
70 cm420 to 450 MHz
33 cm902 to 928 MHz*
23 cm1240 to 1300 MHz
13 cm2300 to 2310 MHz*
13 cm2390 to 2450 MHz*

* Not in the exam

Beyond these, Technicians also have have access to the SHF and EHF (microwave) bands; and CW access only to a three HF bands, plus data & SSB at 10 m.

These are set out in rule 97.301, however, a graphical representation, called a "Band Plan", the 8.5" x 11" ones are suitable for printing at A4, and the one 11" x 17" for A3. See: ARRL Graphical Frequency Allocations

While the plan above is mandated, including use of CW, data, voice, etc, in portions of some bands, there are also "gentlemen's agreement" band plans, recommending frequencies for particular modes (eg, AM at 50.4 MHz) and uses, things such as APRS (Automatic Position Reporting System), meteor scatter, and FM simplex calling at 146.520 & 52.525 MHz.

Polarisation / Polarization

Radio waves, or electromagnetic waves, consist of an electric field and a magnetic field, at 90 degrees to each other. These are "polarised", with the naming in accordance with the polarity of the electric field. The electric field in in line with the the element(s) of the antenna. In most densely populated parts of Australia you will see TV antennas with the elements horizontally. In some areas they are vertical, although many rural areas have gone to UHF only with horizontal polarisation, but often old antennas (or parts thereof) remain on tall masts.

Those who did physics at high school may remember that a current in a wire generates a magnetic field at 90 degrees to the wire. The electric field is at 90 degrees to the magnetic. Remember, the paper asks for electric field, which is in line with the elements.

In VHF and UHF amateur radio FM signals (and related packet radio, APRS, etc) use vertical polarisation, as omni-directional antennas for cars are a simple vertical wire or rod. Yagi antennas can be used, with the elements vertical, typically pointed at a distant FM repeater. For single-sideband (usually USB), the convention is to use horizontal polarity. Between home stations, or when set up as a field-day station this is often achieved using horizontal yagis, or related designs. For mobile stations, halo and similar antennas are often used.

Note that the above is a convention, and it is still possible to use SSB if you only have a vertical antenna. On a line-of-sight path there can be a large (~20 dB) loss between a vertical and horizontal VHF or UHF antenna, but as signals travel, trees, and the like contribute to "de-polarisation" of the signal, meaning a reasonable signal can still be received with cross-polarised antennas. UHF and microwave links can deliberately use differing polarisation as a means to reduce interference. The first hop may be on one channel, the second on a different one, the third on the first channel, but at 90 degrees; or UHF-FM links between two (vertical) repeaters, horizontal.

When communicating via satellite systems, especially low-earth orbiting ones, circular polarisation (CP) is often used; and likewise when reflecting higher-powered signals off the moon. This is generated using yagis with crossed elements stages progressively along the boom, or a spiral (helix) pointing towards the "bird". That said, I helped a school which had VHF and UHF CP yagis for downloading data or "telemetry" from a Russian school's satellite project, and they also worked fine pointing at repeaters around the region.

Ionising / ionizing radiation?

Nytt! Radio waves do NOT have the energy to damage your DNA. What does is when you breath in, or ingest, particles of radio-active material, and these atoms decay or split, releasing huge Alpha particles, Beta particles, or Gamma waves, which can strike an atom within your cell's DNA, perhaps converting it into a mutated, or cancerous cell. Where does this material come from? Some is natural, such as radon gas in the soil, other comes from burning coal, which contains various heavy metals, some radioactive, including uranium. While these are trace amounts, if you burn thousands or millions of tonnes, you get multiple kilograms of this material; a little is left over from Cold War atmospheric nuclear bomb testing. Bananas, for example are rich in vitamin K, or Potassium, a small amount of which is radioactive, but don't let that stop you eating them, it is all about dose. Ultraviolet light is also an example of ionising radiation, but remember, you DO need sunlight to synthesise Vitamin D.

Sample Antennas

Tall 6/8 antenna Left is a Comet SBB-7 dual-band antenna. On 70 cm it is described as
"7.2dBi Three 5/8 waves in phase", and on 2m as "4.5dBi 6/8 wave center-load".
It is 55" (1397 mm) high.

Below is a generic quarter-wave for 2 metres. It may work as a 3/4 antenna on
70 cm, but these have a high angle of radiation with less signal going to the horizon.
It is 19" (483 mm) from nut to tip, or 18" (457 mm) of antenna element, a little shorter
than calculated, but this is how it tuned in a gutter grip mount.

The base is an SO-239 connector, also called "UHF".
It has a a large magnet in the bottom, to retain it on the steel roof of most vehicles.
The magnet is 4" (100 mm) in diameter, and the housing 4 11/16" (119 mm).
It is a little small for the big antenna shown, as while it may stay on a German designed
Holden at the NT limit of 130 km/h (81 MPH), it can be blown over by passing a large
semi-trailer at lower speeds.
The cable is generic RG-58 C/U.
1/4 antenna

Relevant Questions

These are actual questions from the NCVEC question pool.

For regulations questions, numbers in the square brackets are FCC rule the question in about. These are not printed on the exams.

What is the name for the distance a radio wave travels during one complete cycle?
A. Wave speed
B. Waveform
C. Wavelength
D. Wave spread

Wavelength, answer C. Waveform, is the shape of wave, be it sine-wave, square-wave, triangular, sawtooth, trapezoidal, or something more complex, like the human voice, or a violin.

What property of a radio wave is used to describe its polarization?
A. The orientation of the electric field
B. The orientation of the magnetic field
C. The ratio of the energy in the magnetic field to the energy in the electric field
D. The ratio of the velocity to the wavelength

It is the orientation of the electric field, which is in line with the elements of the antenna, answer A.

What are the two components of a radio wave?
A. AC and DC
B. Voltage and current
C. Electric and magnetic fields
D. Ionizing and non-ionizing radiation

This is discussing the radio energy once it has left the transmitting antenna, these are made from electric and magnetic fields, answer C. While in the feedline radio signals are high-frequency AC, not AC and DC, and while they are voltage and current in the feedline, we are discussing radio signals once launched from the antenna. Radio signals are NON-IONIZING only, so do NOT cause cancer, unlike high density ionising radiation, or if you do breath in uranium from the smokestack of a COAL plant (none gets out of a nuclear one, unless it is a badly designed Soviet one which is being abused), and these atoms then undergo fission, releasing radiation directly into your cells.

How fast does a radio wave travel through free space?
A. At the speed of light
B. At the speed of sound
C. Its speed is inversely proportional to its wavelength
D. Its speed increases as the frequency increases

Radio wave travel at the speed of light in free space (a vacuum). This is one of the constants of physics, and does not vary with frequency or wavelength. Answer A.

In a medium, such as glass or water, the creation of colourful spectrums or rainbows is down to speed differences, but the direction of the variation is wrong.

How does the wavelength of a radio wave relate to its frequency?
A. The wavelength gets longer as the frequency increases
B. The wavelength gets shorter as the frequency increases
C. There is no relationship between wavelength and frequency
D. The wavelength depends on the bandwidth of the signal

2 metre signals have a much higher frequency than 80 metre band signals (146 vs 3.6 MHz), so wavelength gets shorter as frequency increases, answer B. This also applies to things like big bassy double-bassoons compared to a tiny piccolo or tin whistle; and likewise to huge low organ pipes and tiny high ones. Bandwidth is how much spectrum is used while sending the signal. This varies from narrow Morse code, or CW signals (officially 100 Hz wide), through voice 2.8 kHz (SSB) to 16 kHz (FM) wide, to full scan TV at up to 7 MHz. The only real challenge with the interaction between bandwidth and wavelength was building high gain single channel antennas for analogue TV, as the wavelength at 45 MHz is different to that at 52 MHz.

What is the formula for converting frequency to approximate wavelength in meters?
A. Wavelength in meters equals frequency in hertz multiplied by 300
B. Wavelength in meters equals frequency in hertz divided by 300
C. Wavelength in meters equals frequency in megahertz divided by 300
D. Wavelength in meters equals 300 divided by frequency in megahertz

Easy: both the wavelength and frequency conversion formulas have the 300 at the top of the division formula, so D. The 300, specifically 300 "megametres", relates to the frequency in megahertz (MHz), and so the two megas cancelling.

What property of radio waves is often used to identify the different frequency bands?
A. The approximate wavelength
B. The magnetic intensity of waves
C. The time it takes for waves to travel one mile
D. The voltage standing wave ratio of waves

Band names, such 10 metres, and 2 metres, are approximate wavelengths! Answer A. Radio waves travel the non-SI statue mile at a constant speed, irrespective of frequency or wavelength. This is: 1609.34 / 299792458 = 0.0000053681804 seconds ≈ 5.368 μs.

What are the frequency limits of the VHF spectrum?
A. 30 to 300 kHz
B. 30 to 300 MHz
C. 300 to 3000 kHz
D. 300 to 3000 MHz

50 and 144 MHZ, along with 222 MHz are the VHF bands, so must be 30 to 300 MHz, answer B. Don't be tricked by the kHz in A, this is the Low Frequency band, also called Long Wave. The other two are Medium Frequency or Medium Wave; and the Ultra High Frequency (UHF) bands. You could also remember VHF airband, around 121.5 MHz, or VHF marine, around 156.8 MHz.

What are the frequency limits of the UHF spectrum?
A. 30 to 300 kHz
B. 30 to 300 MHz
C. 300 to 3000 kHz
D. 300 to 3000 MHz

Same group of answers, but this time D, 300 to 3000 MHz. Examples of our UHF bands are our 440 and 1296 MHz bands; plus UHF CB down-under, at 477 MHz. 13 cm, up to 2450 MHz, is a lower microwave band, also at UHF, and yes, this is the frequency your microwave oven works at.

What frequency range is referred to as HF?
A. 300 to 3000 MHz
B. 30 to 300 MHz
C. 3 to 30 MHz
D. 300 to 3000 kHz

3 to 30 MHz, C for Charlie, which contains the HF bands such as 40 metres (7 MHz).

What is the approximate velocity of a radio wave as it travels through free space?
A. 150,000 kilometers per second
B. 300,000,000 meters per second
C. 300,000,000 miles per hour
D. 150,000 miles per hour

300,000,000 metres per second, answer B. Remember, scientists use SI (metric) systems, not miles.

What is the approximate length, in inches, of a quarter-wavelength vertical antenna for 146 MHz?
A. 112
B. 50
C. 19
D. 12

We can use knowledge that 146 MHz is in the 2 metre band - or get there using 300 / 146 = 2.055 - and quarter this, getting about 50 cm. But not so fast! Collective resistance to change means they want to use units from a country they fought a war to be independent of... There are 2.54 cm in an inch, so 50 / 2.54 = 19.68", nearest to answer C (and real antennas are usually a little less, due to various factors). I suppose the 12 is the number of inches in a foot, and 112 is to trick those remembering answers, as it is the answer to the next Q.

What is the approximate length, in inches, of a 6 meter 1/2-wavelength wire dipole antenna?
A. 6
B. 50
C. 112
D. 236

Half of 6 is 3 metres, or 300 cm, divide this by 2.54 and you get 118 inches, but practical antennas are a bit shorter than this, so 112, answer C. I suppose 6 is the overall wavelength in metres, which converts to 236 ancient units, and 50 MHz is the frequency.

T1B03= [97.301(a)]
Which frequency is within the 6 meter band?
A. 49.00 MHz
B. 52.525 MHz
C. 28.50 MHz
D. 222.15 MHz

Two ways to get the answer: 300 / 6 = 50 MHz, but there are two similar answers, so better to rely in knowing the band runs from 50 to 54 MHz. So 52.525 MHz is the answer, answer B. This frequency is the global FM calling frequency on this band. 49 MHz is an unlicensed low power walkie-talkie band, the others are in other ham bands.

T1B04= [97.301(a)]
Which amateur band are you using when your station is transmitting on 146.52 MHz?
A. 2 meter band
B. 20 meter band
C. 14 meter band
D. 6 meter band

300 / 146.52 = 2.0475 metres, very close to answer A, the name of the popular VHF band. This is the FM calling frequency (simplex) for this band, used because the 30 kHz spacing is used in North America. 6 and 20 m are two other Amateur bands, dunno where 14 comes from, I suppose it is the frequency of the 20 metre band.

T1B05 - T1B07 have been totally changed, and are not maths questions any more.

In which direction is the radiation strongest from a half-wave dipole antenna in free space?
A. Equally in all directions
B. Off the ends of the antenna
C. Broadside to the antenna
D. In the direction of the feed line

Radiation is broadside to the antenna, answer C. If you lower the antenna they radiate upwards so the signal refracts downwards over local area, out to a few hundred kilometres, but this in NOT "in free space". If you transmit at 3 times the frequency at which it is a halfwave (say 21 MHz instead of 7 MHz) there are 4 lobes, and at higher frequencies again, signals do radiate off the ends, but remember, the antenna is NOT a half wave long at these frequencies.

What antenna polarization is normally used for long-distance weak-signal CW and SSB contacts using the VHF and UHF bands?
A. Right-hand circular
B. Left-hand circular
C. Horizontal
D. Vertical

VHF and UHF home and field contest stations using Morse and SSB typically use horizontal yagi antennas, or other horizontal antennas. Rovers, vehicle based stations may use "halo" antennas, looking similar to a netball hoop. Answer C.

What can happen if the antennas at opposite ends of a VHF or UHF line of sight radio link are not using the same polarization?
A. The modulation sidebands might become inverted
B. Signals could be significantly weaker
C. Signals have an echo effect on voices
D. Nothing significant will happen

Note that this is a hilltop to hilltop path, so the answer is B, a significant loss in signal level is likely. However, terrain & trees do tend to depolarise signals. "Echoes" are an HF, and maybe 6m phenomena, where signals travel the long and short path from a station a significant distance away, such as from Australia to UK, both over Asia; and over Antarctica and the up the Atlantic. I can't think of a process which would invert the sidebands between antennas.

On to: Modes

You can find links to lots more on the Learning Material page.

Written by Julian Sortland, VK2YJS & AG6LE, February 2018.

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