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Two Source Interference (CIE AS Physics)

Revision Note

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Demonstrating two source interference

  • 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

Water waves interference fringes, downloadable AS & A Level Physics revision notes

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

path-difference-and-interference-pattern-counting-wavelengths

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 = 
  • 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 experiment, downloadable AS & A Level Physics revision notes

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, downloadable AS & A Level Physics revision notes

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

 creation-of-diffraction-pattern-aqa-al-physics

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

Two source interference fringes

  • 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

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 equations, downloadable AS & A Level Physics revision notes

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

Max and min interference pattern, downloadable AS & A Level Physics revision notes

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

Worked example

Two coherent sources of sound waves S1 and S2 are situated 65 cm apart in air as shown below.WE - Two source interference question image, downloadable AS & A Level Physics revision notes

The two sources vibrate in phase but have different amplitudes of vibration. A microphone M is situated 150 cm from S1 along the line normal to S1 and S2.

The microphone detects maxima and minima of the intensity of the sound. The wavelength of the sound from S1 to S2 is decreased by increasing the frequency.

Determine which orders of maxima are detected at M as the wavelength is increased from 3.5 cm to 12.5 cm.

Answer:

Step 1: Calculate the path difference

  • Using pythagoras' theorem

square root of 65 squared space plus space 150 squared end root space equals space 163

Path difference = 163 space minus space 150 space equals space 13 space cm

Step 2: State the path difference for constructive interference

  • Path difference =
    • n = 0, 1, 2, 3...

Step 3: Determine the wavelength

  • 13 =

n thin space equals space 0 space rightwards double arrow space lambda space equals space 0
n space equals space 1 space space rightwards double arrow space lambda space equals fraction numerator space 13 over denominator 1 end fraction space equals space 13 space cm
straight n space equals space 2 space space space rightwards double arrow space straight lambda space equals fraction numerator space 13 over denominator 2 end fraction space equals space 6.5 space cm
straight n space equals space 3 space space space rightwards double arrow space straight lambda space equals fraction numerator space 13 over denominator 3 end fraction space equals space 4.3 space cm
straight n space equals space 4 space space space rightwards double arrow space straight lambda space equals fraction numerator space 13 over denominator 4 end fraction space equals space 3.3 space cm

  • Only orders 2 and 3 are within the wavelength range of 3.5 cm to 12.5 cm
    • Therefore 2 and 3 are the orders where the maxima are detected

Examiner Tip

The path difference is more specifically how much longer, or shorter, one path is than the other. In other words, the difference in the distances. Make sure not to confuse this with the distance between the two paths.

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Ashika

Author: Ashika

Expertise: Physics Project Lead

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.