AQA A Level Physics复习笔记3.3.1 Path Difference & Coherence

• Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave
• This result is based on the principle of superposition and the resultant waves may be smaller or larger than either of the two individual waves

Coherence

• At points where the two waves are neither in phase nor in antiphase, the resultant amplitude is somewhere in between the two extremes
• Waves are said to be coherent if they have:
  • The same frequency
  • A constant phase difference

   

Coherent v non-coherent wave. The abrupt change in phase creates an inconsistent phase difference

• Coherence is vital in order to produce an observable, or hearable, interference pattern
  • Laser light is an example of a coherent light source, whereas filament lamps produce incoherent light waves
  • When coherent sound waves are in phase, the sound is louder because of constructive interference

   

Path Difference

• Path difference is defined as:

The difference in distance travelled by two waves from their sources to the point where they meet

• Path difference is generally expressed in multiples of wavelength

At point P2 the waves have a path difference of a whole number of wavelengths resulting in constructive interference. At point P1 the waves have a path difference of an odd number of half wavelengths resulting in destructive interference

• In the diagram above, the number of wavelengths between:
  • S1 ➜ P1 = 6λ
  • S2 ➜ P1 = 6.5λ
  • S1 ➜ P2 = 7λ
  • S2 ➜ P2 = 6λ

   

• The path difference at point P1 is 6.5λ – 6λ = λ / 2
• The path difference at point P2 is 7λ – 6λ = λ
• In general:
  • The condition for constructive interference is a path difference of nλ
  • The condition for destructive interference is a path difference of (n + ½)λ
  • In this case, n is an integer i.e. 0, 1, 2, 3...

   

At point P the waves have a path difference of a whole number of wavelengths resulting in constructive interference

• Another way to represent waves spreading out from two sources is shown in the diagram above
• At point P, the number of crests from:
  • Source S1 = 4λ
  • Source S2 = 6λ

   

• The path difference at P is 6λ – 4λ = 2λ
• This is a whole number of wavelengths, hence constructive interference occurs at point P

      ANSWER: B

• At point X:
  • Both peaks of the waves are overlapping
  • Path difference = 5.5λ – 4.5λ = λ
  • This is constructive interference and rules out options C and D

   

• At point Y:
  • Both troughs are overlapping
  • Path difference = 3.5λ – 3.5λ = 0
  • Therefore constructive interference occurs

   

• At point Z:
  • A peak of one of the waves meets the trough of the other
  • Path difference = 4λ – 3.5λ = λ / 2
  • This is destructive interference