Radio waves
Wireless means no cable. The router's antenna makes a radio wave: a ripple of electric and magnetic fields that spreads out in every direction at the speed of light. Your laptop's antenna catches the ripple and reads the bits in it.
Frequency is how many times a wave repeats each second, counted in hertz (Hz). Giga means billion, so Wi-Fi's 2.4 GHz band wiggles about 2.4 billion times every second. The screen shows the wave slowed down enormously.
Wavelength (λ, lambda) is the distance from one crest to the next. It is the speed of light divided by the frequency. At 2.4 GHz that is about 12.5 cm; at 5 GHz, about 6 cm. Higher frequency means shorter waves.
A steady wave carries no news. To send bits, the router changes (modulates) the wave: its height, called amplitude, or where each wiggle starts, called phase. Two heights times two phases give 4 shapes, so each shape carries 2 bits.
Sharing the spectrum
All radio frequencies together are the spectrum, drawn here as a ruler from 0 to 7.5 GHz. Everyone shares the same air, so governments, coordinated worldwide by the ITU, split the ruler into bands and set rules for each band.
A licensed band has one owner. Mobile operators pay for blocks such as 700 MHz, 1800 MHz, 2.6 GHz and 3.5 GHz, and nobody else may transmit there. That keeps your phone's mobile signal clean.
Unlicensed bands are free for anyone who follows the power limits. Wi-Fi uses 2.4, 5 and 6 GHz, and Bluetooth and microwave ovens share 2.4 GHz too. No fee and no licence, but no protection from the neighbours either.
Choosing a band
Waves weaken as they spread, and walls soak up part of them. Higher frequencies lose more: in open air, 5 GHz arrives about 4 times weaker than 2.4 GHz, and walls absorb it more too. So 2.4 GHz reaches further rooms.
Higher up the ruler there is far more room. The whole 2.4 GHz band is 83.5 MHz (million hertz) wide; the 6 GHz band is 1,200 MHz, over 14 times wider. Wider channels fit there, and wider channels carry more bits per second.
Each band is cut into channels. In 2.4 GHz, channel centres sit only 5 MHz apart, but each channel is about 20 MHz wide, so neighbouring channels overlap. Channels 1, 6 and 11 are the usual three that stay clear of each other.
If the neighbour's Wi-Fi uses your channel, the two networks must take turns. On an overlapping channel they garble each other's signals instead. Either way, everyone slows down. Picking 1, 6 or 11, or moving up to 5 or 6 GHz, helps.
The numbers
;; step 1/11 · radio
medium the air (Wi-Fi is IEEE 802.11)
wave an electromagnetic wave, like light but invisible
speed c = 299,792,458 m/s, about 3.34 µs/km in air
(fibre is slower: about 5.0 µs/km, see "Bits on the wire")
both ways the laptop also has a transmitter and answers back
The ruler is drawn to scale from 0 to 7.5 GHz. The waves on the screen and in the room are slowed down billions of times and drawn far longer than real wavelengths. Band edges follow US (FCC) rules where countries differ; the mobile bands are 3GPP examples. Check your own country's regulator for the exact edges and power limits.