Two Source Interference (CIE A Level Physics)

• Two source interference can be demonstrated using
  
  • water waves in a ripple tank
  • sound
  • light
  • microwaves

 

Using water waves

• Two-source interference in can be demonstrated in water using ripple tanks
• A curved line represents each wavefront (peak or trough)
• The diagram below shows the wavefronts from two point sources e.g. dropping two pebbles near to each other in a pond

Wavefront interference

At the blue dot where the peak of two waves meet, constructive interference occurs. At the yellow dot where two troughs meet, constructive interference also occurs. Constructive interference occurs along the lines of maximum displacement. At the green dot, where a peak and a trough meet, destructive interference occurs

• The lines of maximum displacement occur when all the peaks and troughs line up with those on another wave

• On a wavefront diagram, it is possible to count the number of wavelengths to determine whether constructive or destructive interference occurs at a certain point

At point P the waves from S₁ and S₂ have a path difference of a whole number of wavelengths, resulting in constructive interference

• At point P, the number of crests from:
  • Source S₁ = 4λ
  • Source S₂ = 6λ

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

 

Using sound waves

• Two-source interference can be demonstrated with two speakers emitting a coherent sound

Sound wave interference

Sound wave interference from two speakers

• Sound waves are longitudinal waves made up of compressions and rarefactions
  • Constructive interference occurs when the compressions and rarefactions from each wave line up and the sound appears louder
  • Destructive interference occurs when a compression from one wave lines up with a rarefaction from the other and vice versa. The two waves cancel each other out, so zero sound is heard. 
  • This is the technology used in noise-cancelling headphones

 

Using microwaves

• Two-source interference for microwaves (and other electromagnetic waves) can be detected with a moveable microwave detector

Microwave interference experiment

Microwave interference experiment

 

• The detector picks up a maximum amplitude or intensity in regions of constructive interference 
• The detector picks up a minimum or zero amplitude, so no signal in regions of destructive interference 

 

Using light waves

• Lasers are the ideal piece of equipment to analyse diffraction and intensity patterns
• The diffraction pattern produced by a laser on a screen is made up of:
  • Areas of constructive interference - the bright strips or fringes
  • Areas of destructive interference - the dark fringes

 

The constructive and destructive interference of laser light through a double slit creates bright and dark strips called fringes on a screen placed far away

• For two-source interference fringes to be observed, the sources of the wave must be:
  • Coherent (constant phase difference)
  • Monochromatic (single wavelength)

• A laser is an example of a coherent monochromatic light source
  • Other sources of light, such as a filament bulb or a sodium lamp, are non-coherent, so they produce white light

A laser beam

A laser produces a beam of coherent monochromatic light

• When two waves interfere, the resultant wave depends on the phase difference between the two waves
• Phase difference is proportional to the path difference between the waves which can be written in terms of the wavelength λ of the wave
• As seen from the diagram below, the wave from slit S₂ has to travel slightly further than that from S₁ to reach the same point on the screen.
  • The difference in distance is the path difference

Path difference for constructive and destructive interference

Path difference for constructive and destructive interference is determined by wavelength

 

• Remember, the conditions for Constructive and destructive interference:
  • For constructive interference (or maxima), the difference in wavelengths will be an integer number of whole wavelengths
  • For destructive interference (or minima) it will be an integer number of whole wavelengths plus a half wavelength
• An example of the orders of maxima is shown below:
  • n is the order of the maxima/minima since there is usually more than one of these produced by the interference pattern

Double slit interference pattern

Interference pattern of light waves shown with orders of maxima

•  n = 0 is taken from the middle, n = 1 is one either side and so on