Wave Superposition Lab
Stack sine waves and watch them interfere, beat, and stand still — all built on the wave equation v = f·λ.
This is exact wave superposition — every point is the sum of the component waves, no faked envelopes. Pick a preset or add your own waves, then tune amplitude, wavelength, frequency and phase. Identical in-phase waves double up (constructive), opposite phases cancel (destructive), two close frequencies produce beats, and two opposite-direction waves freeze into a standing wave.
Presets
System
Selected wave
Tap a wave chip in the canvas to read its amplitude, wavelength, frequency, period, k, ω and v = f·λ — and adjust it live.
Formulas & sources
y(x,t) = Σ Aᵢsin(kᵢx − ωᵢt + φᵢ)
v = fλ · k = 2π/λ · ω = 2πf
beat = |f₁ − f₂|
node spacing = λ/2
The units and constants behind these waves
One equation, v = f·λ, ties a wavelength you measure in metres to a frequency you count in hertz. Both of those units are defined by fixed constants, so every wave reading here is really a comparison against caesium and the speed of light.
What you are changing
The two constants under v = f·λ
The same equation, from a piano note to red light
| Wave | Frequency | Wave speed | Wavelength |
|---|---|---|---|
| Concert A on a piano | 440 Hz | 343 m/s | 0.780 m |
| The top of human hearing | 20 kHz | 343 m/s | 17.1 mm |
| FM radio | 100 MHz | 299,792,458 m/s | 3.00 m |
| Wi-Fi | 2.4 GHz | 299,792,458 m/s | 0.125 m |
| Red light | 430 THz | 299,792,458 m/s | 697 nm |
Wavelengths are computed live as λ = v/f. Sound uses 343 m/s (dry air at 20 °C); radio and light use the exact speed of light from our constants page.
A frequency reading is a count against caesium
Since 1967 the second has been defined by fixing the caesium-133 hyperfine transition at exactly 9 192 631 770 Hz. A hertz is one cycle per second — so when this lab shows 2 Hz, it means two cycles for every 9 192 631 770 caesium oscillations.
See the seven defining constants →