10.6.1 Nodes and Antinodes

When two waves of the same amplitude and wavelength travelling in opposite directions superpose, the resultant wave is called a standing wave (or stationary wave).

While the resultant wave retains the frequency and wavelength of the superposing waves, the standing wave is different from the travelling waves in many ways.

Propagation

The “wave crest” of a standing does not advance. It stays at the same spot. In fact, overall, there is no net transfer of energy or momentum in either direction. The energy is actually trapped between the ends of the standing wave.

Amplitude

A standing wave has positions called antinodes (AN) where the amplitude (of oscillation) is maximum, and positions called nodes (N) where the amplitude is zero[1]. The segment between two adjacent nodes is called a loop. A loop corresponds to half a wavelength.

Phase

All the oscillations in the same loop are completely in phase. On the other hand, adjacent loops are in antiphase. So, two points on a standing wave are either completely in phase, or completely out of phase with each other.

The table below provides a summary.

 Traveling WaveStanding Wave
PropagationWave crest advances. Energy is transferred in the direction of wave travel.Wave crest does not advance. Energy is trapped between the ends of the standing wave.
AmplitudeUniform. Same amplitude at every point in the wave.Not uniform. Zero at the nodes, maximum at the antinodes.
PhaseEach point progressively lags the preceding point.
\displaystyle \Delta \theta =\frac{{\Delta x}}{\lambda }\times 2\pi
All points of the same loop are in-phase. All points of one loop are in antiphase with all points of the adjacent loops.
\displaystyle \Delta \theta \ne \frac{{\Delta x}}{\lambda }\times 2\pi

Animation

Formation, Nodes and Antinodes

Concept Test

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[1] You may realize that antinodes are formed at locations where the two waves travelling in opposite directions meet in phase. Nodes are formed at locations where the two waves meet in antiphase.

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