A Wi-Fi signal is a wave. Its frequency, wavelength and phase explain why it travels the way it does, why antennas are the size they are, and why moving a laptop a few centimetres can change the signal.
1. DefinitionWhat is a radio wave?
A radio wave is a pattern of electric and magnetic fields that moves through space at the speed of light. Radio waves, infrared, visible light and X-rays are all the same kind of thing at different frequencies. A Wi-Fi radio makes a steady wave called the carrier and then changes it, a little at a time, to carry data (that is modulation).
- Frequency (f) is how many complete cycles happen each second. One cycle per second is one hertz (Hz); Wi-Fi uses millions (MHz) and billions (GHz) of cycles per second.
- Period (T) is the time one cycle takes: T = 1 / f.
- Wavelength (λ) is the distance the wave travels during one cycle: λ = c / f, where c is the speed of light.
- Amplitude is the height of the wave, how strong it is. Power is proportional to amplitude squared.
- Phase is how far through its cycle the wave is at a given moment or place, in degrees. A full cycle is 360 degrees.
2. PurposeWhy start with waves?
- Wavelength sets the size of things. An antenna works best when it is a sensible fraction of a wavelength. At 2.4 GHz that is a few centimetres, which is why a Wi-Fi antenna fits in a phone.
- Wavelength decides how a wave meets obstacles. Objects much smaller than a wavelength barely disturb it; large flat surfaces such as walls and floors reflect it; edges bend (diffract) it.
- Phase decides what happens when waves meet. The same two waves can reinforce each other or cancel, depending only on how far each one travelled.
- It is the root of the band topics. Everything about 2.4, 5 and 6 GHz that depends on frequency starts from the relationship between frequency and wavelength.
3. MechanismFrequency, wavelength and period
The wave below is drawn over three wavelengths. Slide the frequency up and the wavelength shrinks; the distance scale underneath is real. Use the buttons to jump to a real frequency. Change the amplitude and phase to see what each does.
Try this. (1) Select FM radio, then 2.4 GHz: the wavelength falls from about 3 m to about 12 cm. (2) Double the frequency and watch the wavelength halve. (3) Set the amplitude to 10 and read the power: it is 100 times the power at amplitude 1, because power follows the square.
4. VisualWhat happens when two waves meet
A receiver does not hear the direct wave and its echoes separately: it senses their sum. Add two waves point by point. If they rise and fall together they reinforce each other (constructive). If one rises while the other falls they cancel (destructive). Which one you get depends on the extra distance the echo travelled, measured in wavelengths.
Try this. Set the echo strength to 100%, then slide the extra distance from 0 to about 6 cm at 2.4 GHz. The sum shrinks to almost nothing at half a wavelength (6.2 cm), then recovers at a full wavelength (12.3 cm). Now switch to 5 GHz: the same movement is a much bigger share of a wavelength, so the swings are faster.
5. MathematicsThe formulas, with numbers
Wavelength. λ = c / f. For channel 6 in 2.4 GHz, f = 2437 MHz, so λ = 299 792 458 / 2 437 000 000 = 0.1230 m, or 12.3 cm. The period is T = 1 / f = 0.410 ns.
| Signal | Frequency | Wavelength | Period |
|---|---|---|---|
| FM radio (about 100 MHz) | 100 MHz | 3.00 m | 10.00 ns |
| 2.4 GHz, channel 6 (2437 MHz) | 2437 MHz | 12.30 cm | 0.41 ns |
| 5 GHz, channel 100 (5500 MHz) | 5500 MHz | 5.45 cm | 0.18 ns |
| 6 GHz, channel 37 (6135 MHz) | 6135 MHz | 4.89 cm | 0.16 ns |
Phase and distance. A wave that has travelled an extra distance d is behind by 360 × d / λ degrees. At 2437 MHz an extra 6.15 cm is half a wavelength, 180 degrees. Adding two waves of amplitudes A1 and A2 with phase difference δ gives a wave of amplitude sqrt(A12 + A22 + 2A1A2cos δ). With two equal waves that is 2A when δ = 0 (four times the power, +6 dB) and 0 when δ = 180 degrees.
Worked example. A direct wave of amplitude 1 and an echo of amplitude 0.8 arrive 180 degrees apart. The sum is sqrt(1 + 0.64 – 1.6) = sqrt(0.04) = 0.2: the signal falls to a fifth of its amplitude, which is 20 log10(0.2) = -14 dB, from an echo that is itself weaker than the direct wave.
6. Real-world behaviourMultipath, fading and why wavelength matters
- Multipath fading. Indoors a signal reaches the receiver by many paths (direct, off walls, floors and furniture). Their sum changes with position on the scale of a wavelength, so signal strength can swing by many dB over a few centimetres. Moving the antenna a little can fix a weak spot.
- Why bands behave differently. A shorter wavelength means the pattern of fades repeats over a shorter distance, and the wave is more easily blocked by objects that are large compared with it.
- Why it is not just distance. Two clients at the same distance from an access point can see very different signal strength, because each sits at a different point in the interference pattern.
Practical validationProve it in a capture and on a spectrum analyser
Reading about a band is one thing; seeing it in your own evidence is the skill. These checks work with any monitor-mode capture:
- Pick a channel from the table above and work out its wavelength yourself with λ = c / f. Check it against the model.
- Start a monitor-mode capture and look at the
radiotap.dbm_antsignalfield of frames from one access point. Move the receiving antenna about half a wavelength (6 cm at 2.4 GHz) and see how much the value changes. - Question to answer: at 5 GHz, how far must an echo travel beyond the direct path to arrive exactly half a cycle behind?
Check your understandingQuick quiz
ReferencesSources and further reading
- NIST CODATA: speed of light in vacuum, 299 792 458 m/s (exact)
- BIPM: The International System of Units (SI Brochure), including units for logarithmic ratio quantities
- IEEE 802.11 Working Group
The relationships on this page (wavelength, period, phase and the sum of two sine waves) are standard physics rather than amendments of 802.11. The speed of light is exact by the definition of the metre. Channel centre frequencies are defined in IEEE 802.11 and are covered in the band topics.