Superposition: (i) the principle of superposition of waves

The idea

The principle of superposition states that when two or more waves meet at a point, the resultant displacement at that point equals the vector sum of the individual displacements of each wave. Displacement is a vector, so direction matters: crests meeting crests add to give a larger displacement, while a crest meeting a trough can partially or completely cancel. For example, two identical waves each of amplitude 2.0 cm arriving in phase produce a resultant amplitude of 4.0 cm; arriving in antiphase they produce zero resultant displacement. The principle applies to all wave types, including sound, light and microwaves, and underlies interference patterns. It applies at every instant, so the resultant displacement changes as the waves move.

What earns the marks

• States that at a point where waves meet, the resultant displacement is the vector sum of the individual displacements.
• Recognises that displacement is a vector quantity, so the direction of each wave's displacement must be taken into account.
• Applies the principle to give constructive superposition when displacements are in the same direction, producing a larger resultant amplitude.
• Applies the principle to give destructive superposition when displacements are in opposite directions, producing a smaller or zero resultant.
• Applies the principle to sound, light and microwave waves, not only to waves on strings or water.

Common mistakes and how to put them right

• Adding amplitudes arithmetically without considering direction.

  Put it right: Displacements must be summed as vectors, so opposite displacements subtract.

• Believing waves are destroyed or absorbed when they cancel.

  Put it right: The waves continue to travel and carry energy, only the resultant displacement at that point is reduced.

• Thinking superposition only applies to identical waves.

  Put it right: It applies to any waves meeting at a point, whatever their amplitudes or frequencies.

• Assuming the resultant displacement is fixed in time.

  Put it right: It changes continuously as each wave's displacement at the point changes.

Exam tips

• Sketch the two displacements at the same instant before combining them, so direction is explicit.
• Use the terms 'in phase' and 'antiphase' precisely when describing constructive and destructive superposition.
• Check whether the question asks about displacement or amplitude; they are related but not identical quantities.