Two-point source interference

The set-up

• Two-point source interference happens when two sources send out waves that overlap.
• For a steady, observable pattern the two sources must be coherent:
  • the same frequency (and therefore the same wavelength),
  • a constant phase relationship — usually "in phase", meaning they produce crests at the same instant.
• In the laboratory this is done with two dippers driven by the same motor in a ripple tank, or two loudspeakers driven by one signal generator.

Constructive and destructive interference

The pattern is just superposition applied continuously at every point:

• Constructive interference — the two waves arrive in phase (crest meets crest, or trough meets trough).

  • The displacements add, giving a large amplitude.
  • For water: large waves. For sound: loud. For light: bright.

• Destructive interference — the two waves arrive completely out of phase (crest meets trough).

  • The displacements subtract, giving a small or zero amplitude.
  • For water: flat water. For sound: quiet. For light: dark.

• Which happens at a point depends on the path difference — how much further one wave has travelled than the other:

  • paths differing by a whole number of wavelengths → the waves are back in step → constructive,
  • paths differing by a half number of wavelengths ($\tfrac{1}{2}\lambda$, $1\tfrac{1}{2}\lambda$, …) → the waves are exactly out of step → destructive.

• At Level 2 you explain this qualitatively — you are not asked to calculate fringe spacings.

The pattern that results

• The regions of constructive and destructive interference are not scattered — they form lines radiating outward from between the two sources.
  • Antinodal lines — lines of constructive interference (large amplitude).
  • Nodal lines — lines of destructive interference (little or no amplitude).
• They alternate: antinodal, nodal, antinodal, and so on out to each side.
• The central line, exactly midway between the two sources, is always antinodal.
  • Every point on it is equidistant from both sources, so the path difference is zero — the waves always arrive in phase there.

Move the two sources and change the wavelength below, and watch the nodal and antinodal lines shift:

How the pattern changes

Two changes are examined repeatedly:

• Increasing the wavelength (equivalently, lowering the frequency):
  • the lines spread further apart,
  • fewer lines fit into the same region.
• Increasing the separation of the sources:
  • the lines are squeezed closer together,
  • more lines fit into the same region.
• Stated as one rule: the spacing of the pattern grows with wavelength and shrinks with source separation.
• Changing the amplitude of the sources changes how strong the effect is, but not where the nodal and antinodal lines lie.

What interference is not

• It is not waves cancelling energy out of existence. Energy is redistributed — removed from the nodal lines and concentrated on the antinodal lines. Total energy is unchanged.
• It is not the same as diffraction, though the two often appear together. Diffraction is one wave spreading through a gap; interference is two waves overlapping.