4.3.3 Superposition

• The principle of superposition states that:

When two or more waves meet, the resultant displacement is the vector sum of the displacements of the individual waves 

• The principle of superposition applies to both transverse and longitudinal waves
• Interference occurs whenever two or more waves superpose
• For a clear stationary interference pattern, the waves must be of the same:
  • Type
  • Amplitude
  • Frequency
• They must also have a constant phase difference

Constructive & Destructive Interference

• Constructive interference occurs when the waves superpose and have displacements in the same direction (both positive or both negative)
• Destructive interference occurs when the waves superimpose and have displacements in opposite directions (one positive and one negative)
• When two waves with the same amplitude meet at a point, they can:
  • Be in phase and interfere constructively, so that the displacement of the resultant wave is double the displacement of each individual wave
  • Be in anti-phase and interfere destructively, so that the displacement of the resultant wave is equal to zero

Waves in superposition can undergo constructive or destructive interference

• Superposition occurs for any two waves or pulses that overlap, and can result in a mix of constructive and destructive interference
  • For example, the peak of one wave superposes with the peak of another wave with a smaller displacement
  • The resultant peak will have a displacement that is in the middle of the displacement of both waves

• Superposition can also be demonstrated with two pulses
  • When the pulses meet, the resultant displacement is the algebraic sum of the displacement of the individual pulses
  • After the pulses have interacted, they then carry on as normal