Send two identical waves toward each other and they superpose into a pattern that does not travel: fixed points that never move and points that swing wildly. This is the physics of every string and pipe that makes a musical note.
By the principle of superposition, when two waves meet, the resultant displacement is the sum of the individual displacements. Two waves of the same frequency travelling in opposite directions form a stationary wave: points of permanent zero amplitude (nodes) and points of maximum amplitude (antinodes). Adjacent nodes are half a wavelength apart, and a stationary wave stores energy rather than transferring it along its length.
Step through the harmonics of a string fixed at both ends and watch nodes stay still while antinodes oscillate. The spacing of the nodes gives the wavelength.
The fixed geometry of a stationary wave.
| Feature | Amplitude | Note |
|---|---|---|
| node | permanent zero amplitude | adjacent nodes λ/2 apart |
| antinode | maximum amplitude | halfway between nodes |
| energy | stored, not transferred | no net energy flow along the wave |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
A stationary wave is formed when two waves of the same frequency travel:
On a stationary wave, a point of permanent zero amplitude is called a:
The distance between two adjacent nodes on a stationary wave is:
Unlike a progressive wave, a stationary wave does not:
Stationary waves form wherever waves reflect and overlap.
Adjacent nodes are half a wavelength apart, not a whole wavelength, so the wavelength is twice the node spacing. A stationary wave does not travel and transfers no net energy along its length, unlike a progressive wave. At a node the two waves are always in antiphase, giving permanent cancellation, while at an antinode they reinforce.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
Adjacent nodes on a stationary wave are 0.30 m apart. The wavelength of the waves is:
A string fixed at both ends vibrates in its fundamental mode (first harmonic). The total number of nodes, including the two ends, is:
A pipe closed at one end resonates with a node at the closed end and an antinode at the open end. The shortest length that resonates with sound of wavelength λ is:
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