Sine Wave Explorer

Every radio signal, Wi-Fi included, is built from sine waves. Change the amplitude, frequency, wavelength and phase to see what each one means, then add a second wave to see how two waves add up or cancel out.

Amplitude
Frequency
GHz
Wavelength
cm
Wi-Fi bands

One sine wave

The wave, drawn along the direction it travels Wavelength and amplitude ● A fixed point: it only moves up and down, once per cycle

Two waves: phase

A second wave with the same frequency, shifted by a phase. Where the two waves line up they add together (constructive); where one is up while the other is down they cancel (destructive). Radio waves meet like this whenever a signal arrives by two paths, such as a direct path and a reflection.

Phase of wave 2
Quick picks
Amplitude of wave 2
Wave 1 Wave 2 Wave 1 + wave 2 (what a receiver actually sees) The biggest the sum could be ()

Each wave as an arrow: its length is the amplitude and its angle is the phase. Put the arrows tip to tail and the black arrow is the sum.

The calculation, step by step

Notes

Amplitude

How tall the wave is: the peak strength of the signal. Power goes with the square of the amplitude, so halving the amplitude leaves a quarter of the power, which is 6 dB less.

Frequency and wavelength

Frequency is how many complete cycles pass a point each second. Wavelength is the distance from one crest to the next. Radio waves all travel at the speed of light, so the two are locked together: λ = c ÷ f. Double the frequency and the wavelength halves. That's why a 2.4 GHz wave is about 12.5 cm long and a 5 GHz wave only about 6 cm.

Phase

Where a wave is in its cycle, measured in degrees: 360° is one full cycle. Phase only means something when you compare two waves. A wave that has travelled one extra half-wavelength arrives 180° out of phase; one extra whole wavelength brings it back to 0°.

Why this matters for Wi-Fi

Multipath: indoors, the signal reaches the receiver directly and by reflections off walls, floors and furniture. Each copy arrives with a different phase. Moving a phone a few centimetres (a fraction of a wavelength) can turn a strong spot into a weak one.

Beamforming: an access point with several antennas adjusts the phase of each one so the copies arrive in phase at the client, adding up. See the Beamforming Simulator.

Modulation: Wi-Fi sends data by changing the amplitude and phase of its waves. See the Wi-Fi Modulation Simulator.

About the animation

Real Wi-Fi waves cycle billions of times a second, far too fast to see. The animation is slowed down by the factor shown on the first chart, but keeps the right proportions: a higher frequency still cycles faster, and every wave travels at the same speed.