Two sources of microwaves P and Q produce coherent waves with a phase difference of 180°.

Q#24 (Past Exam Paper – November 2018 Paper 12 Q29)

Two sources of microwaves P and Q produce coherent waves with a phase difference of 180°.

The waves have the same wavelength λ.




At the point S there is a minimum in the interference pattern produced by waves from the two sources. The distance (QS – PS) is called the path difference.

In the expressions shown, is an integer.

Which expression represents the path difference?
nλ                             
½ nλ                        
(+ ½) λ                             
(2+ ½) λ




Solution:
Answer: A.

When 2 sources of waves that are in phase interfere:

Constructive interference (maxima): path difference = nλ     where n is an integer

Destructive interference (minima): path difference = (n+1) λ / 2


However, if the sources has a phase difference of 180°, the above conditions no longer hold for constructive and destructive interference. The conditions are reversed.

Constructive interference (maxima): path difference = (n+1) λ / 2

Destructive interference (minima): path difference = nλ


A minima is produced at S, indicating that destructive interference occurs.  So, path difference = nλ.

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