Two Source Interference (CIE A Level Physics)

• 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

Wavefront interference

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

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

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

Light interference experiment

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 for constructive and destructive interference

Path difference for 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:

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