Standing Waves & Harmonics
Visualize standing wave patterns on strings and in pipes. Select harmonics to see nodes, antinodes, wavelength, and frequency for each resonant mode.
Wave Parameters
Properties
| Mode | Fixed String |
| Harmonic | 1 |
| Length | 1.00 m |
| Wavelength | -- |
| Frequency | -- |
| Wave Speed | 340 m/s |
| Nodes | -- |
| Antinodes | -- |
The Physics Behind It
Standing Wave Formulas
- Fixed string / open pipe: ฮป = 2L/n, f = nv/(2L)
- Closed pipe (odd n only): ฮป = 4L/n, f = nv/(4L)
- Standing wave equation: y(x,t) = 2A sin(kx) cos(ฯt)
- Nodes occur at sin(kx) = 0
- Antinodes occur at |sin(kx)| = 1
Key Concepts
- Standing waves form when two identical waves travel in opposite directions and interfere, creating fixed nodes and antinodes
- Harmonics are the resonant frequencies at which standing waves form: n=1 is the fundamental, n=2 the second harmonic, etc.
- Closed pipes only support odd harmonics because one end is a node and the other is an antinode
- Musical instruments produce specific harmonics depending on their boundary conditions
You're crushing it!