OCR AS Physics

Revision Notes

4.9.3 Interference

Interference

Interference

  • 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
    • The resultant waves may be smaller or larger than either of the two individual waves
  • When two waves with the same frequency and amplitude arrive at a point, they superpose either:
    • In phase, causing constructive interference. The peaks and troughs line up on both waves and the resultant wave has double the amplitude
    • In anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

Constructive and destructive, downloadable AS & A Level Physics revision notes

Waves in superposition can undergo constructive or destructive interference

  • The principle of superposition applies to all types of waves i.e. transverse and longitudinal, progressive and stationary

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, downloadable AS & A Level Physics revision notes

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 a wavelength

Path Difference & Interference Pattern, downloadable AS & A Level Physics revision notes

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 =

Phase Difference

  • Two waves with a path difference will also have a difference in phase
    • This is their phase difference
  • Phase difference is defined as:

The difference in phase between two waves that arrive at the same point

  • It is given as an angle, in radians or degrees

 

Exam Tip

Think of ‘constructive’ interference as ‘building’ the wave and ‘destructive’ interference as ‘destroying’ the wave.

Constructive & Destructive Interference

  • Whether two waves will constructively or destructively interfere at a point is determined by its path difference or phase difference

Path Difference

  • Path difference is determined in multiples of a wavelength
  • Constructive interference occurs when there is a path difference of
    • For example, 2λ
  • Destructive interference occurs when there is a path difference of (n + ½)λ
    • For example, 3λ / 2 or 1.5λ
  • In this case, n is an integer i.e. 1, 2, 3…

Path Difference, downloadable AS & A Level Physics revision notes

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
    • Therefore, this is destructive interference (half-wavelength difference)
  • The path difference at point P2 is 7λ – 6λ = λ
    • Therefore, this is constructive interference (a whole number of wavelengths difference)

Phase Difference

  • The phase difference between two waves is determined by an angle, in radians or degrees
  • Constructive interference occurs when the phase difference is an even multiple of π or that they are in phase
    • Eg. 2π, 4π
  • Destructive interference occurs when the phase difference is an odd multiple of π or that they are in anti-phase
    • Eg. π, 3π

Worked Example

The diagram shows the interferences of coherent waves from two point sources.

WE - Interference and coherence question image 1, downloadable AS & A Level Physics revision notes

Which row in the table correctly identifies the type of interference at points X, Y and Z.

WE - Interference and coherence question image 2, downloadable AS & A Level Physics revision notes

      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

Exam Tip

Remember, interference of two waves can either be:

  • In phase, causing constructive interference
    • The peaks and troughs line up on both waves
    • The resultant wave has double the amplitude
  • In anti-phase, causing destructive interference
    • The peaks on one wave line up with the troughs of the other
    • The resultant wave has no amplitude

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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