The path difference for the constructive interference is:
Correct answer: E. n λ
- A. (n-1)λ
- B. (n+1)λ
- C. n λ / 2
- D. 2n λ
- E. n λ
Explanation
Option A: (n-1)λ: This is the path difference for destructive interference. When the path difference is one wavelength less than a whole number of wavelengths, the waves will be out of phase and will cancel each other out. Option B: (n+1)λ: This is also the path difference for destructive interference. When the path difference is one wavelength more than a whole number of wavelengths, the waves will be out of phase and will cancel each other out. Option C: nλ/2: This is the path difference for a node. A node is a point where the waves cancel each other out completely. Option D: 2nλ: This is not possible, as the path difference cannot be greater than the wavelength of the wave. Option E: The path difference for constructive interference is nλ, where n is any integer. This means that the difference in the distance traveled by two waves must be a whole number of wavelengths. When this happens, the waves will be in phase and will add together to create a larger wave.
This question appeared on the NUMS 2018 paper, which you can sit online with every answer explained.
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About Superposition and Interference
Superposition states that overlapping waves produce a resultant displacement equal to the algebraic sum of their individual displacements. Interference covers constructive and destructive interference, phase difference, path difference, coherent sources, and conditions for maxima and minima. It differs from diffraction, which involves spreading around openings or obstacles.
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