superposition and coherence

• the principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements.
• constructive interference is when two waves combine to form a wave with a larger amplitude.

  destructive interference is when the displacements of two waves cancel each other out. total destructive interference when the displacements of two waves completely cancel eachother out.
• superposition is when two waves meet and the energy is shared between them
• two points on a wave are in phase if they are both at the same point in the wave cycle. points in phase have the same displacement and velocity.

  in the picture, points A and B are in phase, and points A and C are out of phase

  
• one complete cycle of a wave can be represented as an angle of 360 degrees, or by 2pi radians
• two points with a phase difference of zero or a multiple of 360 degrees are in phase.

  points with a phase difference of odd number multiples of 180 are exactly out of phase.

  two different waves can also be in phase, usually if they are both from the same oscillator.
• in order to get clear interference patterns, the sources must be coherent and in phase

  • two sources are coherent if they have the same wavelength and frequency, and have a fixed phase difference between them
• path difference is the amount by which the path travelled by one wave is longer than the path travelled by the other wave.

  • constructive interference occurs when path difference = n$\lambda$
  • destructive interference occurs when path difference = (n+0.5)$\lambda$