Interference

Definitions

• Two waves (of the same wavelength) are said to be in phase if the crests (and troughs) of one wave coincide with the crests (and troughs) of the other, as in Fig. 22.8.
  
    

  Figure 22.8: Constructive interference

  
  
  

  In this case the resultant wave would have twice the amplitude of the individual waves - one says that constructive interference has occurred.

• If the crest of one wave coincides with the trough of the second, as in Fig. 22.9 they are said to be completely out of phase,.
  
    

  Figure 22.9: Destructive interference

  
  
  

  In this case the two waves would cancel each other out - one says that destructive interference has occurred. At a point of constructive interference the net amplitude of the two waves is a maximum, whereas at a point of destructive interference, the net amplitude is a minimum. Of course, one could also have situations in between these two extremes.

Idea: If two identical waves of wavelength $\lambda$ start out in phase, travel at the same speed for a distance of r₁ and r₂ respectively, where r₁ > r₂ , the crests of the one wave will be behind the crests of the other by a distance of r₁ - r₂ . The condition for constructive interference when the waves recombine is

r₁ - r₂ = m$$\lambda$$ ,m = 1,2,....

The condition for destructive interference is

r₁ - r₂ = (m + $${1\over 2}$$)$$\lambda$$ ,m = 1,2,...