8.2.3 Two Source Interference

• Interference of sound, light and microwaves can be demonstrated with slits or diffraction gratings

Using Water Waves

• Two-source interference in can be demonstrated in water using ripple tanks
• The diagram below shows diffracted circle shaped water waves from two point sources eg. dropping two pebbles near to each other in a pond

Water waves interference pattern from a ripple tank

• The two waves interfere causing areas of constructive and destructive interference
• The lines of maximum displacement occur when all the peaks and troughs line up with those on another wave

Using Sound Waves

• Two source interference for sound waves looks very similar to water waves

Sound wave interference from two speakers

• Sound waves are longitudinal waves so are made up of compressions and rarefactions
• Constructive interference occurs when two compressions or two rarefactions line up and the sound appears louder
• Destructive interference occurs when a compression lines up with a rarefaction and vice versa. The sound is quieter
  • This is the technology used in noise-cancelling headphones

Using Microwaves

• Two source interference for microwaves can be detected with a moveable microwave detector

Microwave interference experiment

• Constructive interference: regions where the detector picks up a maximum amplitude
• Destructive interference: regions where the detector picks up no signal

Using Light Waves

• For light rays, such as a laser light through two slits, an interference pattern forms on the screen

Laser light interference experiment

• Constructive interference is shown as bright fringes on the screen
  • The highest intensity is in the middle

• Destructive interference is shown as the dark fringes on the screen
  • These have zero intensity

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

• When two waves interfere, the resultant wave depends on the phase difference between the two waves
• This 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, 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 of constructive and destructive interference is determined by wavelength

• 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
  • n is the order of the maxima/minima since there is usually more than one of these produced by the interference pattern

• An example of the orders of maxima is shown below:

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