Node (wave)
A node is a point in a standing wave where the displacement of the medium is permanently zero due to destructive interference between the two superposed waves. Nodes remain stationary regardless of time, and they occur at intervals of half a wavelength (λ/2) along the medium. In a vibrating string fixed at both ends, the fixed endpoints are always nodes, and the number of nodes determines the harmonic mode of vibration.
Nodes in Different Harmonic Modes (String Fixed at Both Ends)
| Mode | Harmonic Number | Number of Nodes | Number of Antinodes |
|---|---|---|---|
| Fundamental | 1 | 2 | 1 |
| 2nd harmonic | 2 | 3 | 2 |
| 3rd harmonic | 3 | 4 | 3 |
| 4th harmonic | 4 | 5 | 4 |
| nth harmonic | n | n + 1 | n |
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Related Terms
Standing Wave
A standing wave is a wave pattern formed by the superposition of two identical waves travelling in opposite directions, resulting in a stationary pattern of nodes (zero displacement) and antinodes (maximum displacement). Standing waves do not transport energy along the medium; instead, energy oscillates between kinetic and potential forms at fixed positions. They are fundamental to the physics of musical instruments, laser cavities, and microwave resonators.
Antinode
An antinode is a point in a standing wave where the displacement of the medium reaches its maximum amplitude, caused by constructive interference between the two superposed waves. Antinodes oscillate with the greatest energy in the standing wave pattern and are located exactly halfway between consecutive nodes, at intervals of half a wavelength. They are the positions of maximum vibration in musical instrument strings and air columns.
Wavelength
Wavelength is the spatial distance between two consecutive points that are in the same phase of a wave, such as crest to crest or trough to trough. It is denoted by the Greek letter lambda (λ) and measured in metres. Wavelength is inversely related to frequency: higher-frequency waves have shorter wavelengths, which is why X-rays (short λ) are more energetic than radio waves (long λ).
From Latin "nodus" (knot). The term was used because nodes resemble knots in a rope — fixed points where the medium does not move.