Superposition and interference

Superposition

  • Principle of superposition: when two or more waves meet at a point, the resultant displacement is the sum of the displacements of the individual waves.
  • A wave can be represented by a series of vectors.
  • When you add the waves, add the vectors

Phase

  • Two waves are in phase when their peaks and troughs at exactly the same time
  • They are out of phase when they occur at different times

Constructive interference

  • Occurs when two waves combine to give a larger wave
  • This is at a maximum when two waves are in phase

Destructive interference

  • When two waves combine to give a smaller wave
  • This is at a maximum when the path difference is a multiple of .5 of a wavelength
  • They are 180o out of phase

Noise cancelling headphones

  • The headphones creates sound waves that cancel the external noise
  • It is a destructive interference

Beats

  • If two waves of equal amplitude but slightly different frequency combine, the resulting sound wave will pulse like a beat
  • When the waves are in phase, there is constructive interference, when they are out, there is destructive
  • Beats per second = difference in frequencies (|f1-f2|)

Interference – two point sources

  • When waves from two point sources interact, superposition occur
  • Antinodes occur where the waves add, constructive interference. They form antinodal lines
  • Nodes occur when the waves subtract, usually equalling, destructive interference. They form nodal lines.

Two speakers

  • When two speaker produce sound antinodal lines occur where there is constructive interference (loud sound)
  • Nodal lines occur where there is destructive interference (soft sound)

 

 

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