Standing Waves Explorer
See how standing waves form from two interfering waves. Adjust the harmonic number to see overtones.
Orthogonal Eigenfunctions 🖖
Standing waves are solutions to the wave equation under Dirichlet boundary conditions...
Two waves that trap themselves 🖖
A standing wave isn't really going anywhere. It appears when a moving wave bounces off a boundary and overlaps its own reflection: the two travel in opposite directions and lock into a pattern that stays put, with the nodes never budging. Only wavelengths that fit a whole number of half-loops between the ends survive. Takeaway: shorten the string or pipe and those surviving wavelengths shrink, so the pitch climbs.
Your microwave can measure light's speed 🖖
A microwave oven fills its cavity with a standing electromagnetic wave, so energy piles up at fixed antinodes while the nodes stay cold — which is exactly why the food needs a turntable. Remove it, melt a flat bar of chocolate, and the molten patches mark the antinodes about 6 cm apart. Multiply that half-wavelength by the 2.45 GHz printed on the back and you recover c ≈ 3 × 10⁸ m/s on your kitchen counter.
Example problems
- Fundamental - Fundamental mode: 1 antinode
- 3rd harmonic - 3rd harmonic: 3 antinodes
- Open pipe - Open pipe fundamental
- Guitar 2nd - Guitar string 2nd harmonic