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4.9.9Electrons, Waves and Photons

Nodes and Antinodes

5 min read 5 parts Lesson 62 of 62 Unit quiz

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Section 1 of 5Definitions

4.9.9 Nodes and Antinodes
Node
  • A node is a point where the two superposed waves are always in antiphase, so the displacement is permanently zero.
Antinode
  • An antinode is a point where the waves are always in phase, so the oscillation has its largest amplitude.
Spacing
  • Adjacent nodes and adjacent antinodes are each separated by half a wavelength.
Alternating
  • A node lies exactly midway between two neighbouring antinodes, one quarter of a wavelength from each.

Section 2 of 5Behaviour at a Boundary

Behaviour at a Boundary
Fixed end of a string
  • A node forms at a fixed end, since the string cannot move there.
Closed end of a pipe
  • Air cannot move past a closed end, so a displacement node forms there.
Open end of a pipe
  • Air moves freely at an open end, so an antinode forms near that end.
Free end
  • A string end that is free to move would instead be an antinode.

Section 3 of 5Using the Pattern

1
Measure the distance between several neighbouring nodes and divide by the number of gaps to get half a wavelength.
2
Double that distance to obtain the wavelength λ of the progressive waves forming the pattern.
3
Find the frequency from the signal generator or the vibrator setting.
4
Calculate the wave speed using v = fλ and compare it with the expected value.

Section 4 of 5Worked Example

Question

  • Nodes on a stretched string are 0.15 m apart when it is driven at 800 Hz.
  • Calculate the wave speed.

  1. Node spacing = λ ÷ 2, so λ = 2 × 0.15 = 0.30 m.
  2. v = fλ = 800 × 0.30.
    What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)

Answer v = 240 m/s.

Section 5 of 5Exam Checklist & Tips

4.9.9 – Key Points for the Exam

  • Node A point of zero amplitude on a stationary wave.
  • Antinode A point of maximum amplitude on a stationary wave.
  • Half wavelength The distance between two adjacent nodes or antinodes.
  • Displacement node A position in a sound wave where air molecules do not move.

Common Mistakes

  • Taking the node-to-node distance as one full wavelength; it is only half.
  • Counting the end nodes as extra spacings; N nodes give N − 1 gaps.
  • Describing a node as a place where the wave is not present; the waves are present but cancel.
  • Placing a node at an open pipe end; that end is close to an antinode.
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