Problem: Two waves shown below with the same amplitude, A, and wavelength, λ, and traveling in the same direction Initially the sources (dot at the origin) are also at the same point. The source of the second wave is then displaced by a distance δx. (a) For what values of δx will the superposition of the two waves show total constructive interference? Give at least two values in terms of λ.(b) For what values of δx will the superposition of the two waves show total destructive interference? Give at least two values in terms of λ.

🤓 Based on our data, we think this question is relevant for Professor Arratia Munoz's class at UCR.

FREE Expert Solution

For two travelling waves that superimpose into one another;

Interference occurs when the phase difference (angular separation) between the waves is either 0 or π (180°).

Phase difference, ϕ=2πλ(path difference, x)Path difference, x=λ2π(Phase difference, ϕ)

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Problem Details

Two waves shown below with the same amplitude, A, and wavelength, λ, and traveling in the same direction Initially the sources (dot at the origin) are also at the same point. The source of the second wave is then displaced by a distance δx. 

(a) For what values of δx will the superposition of the two waves show total constructive interference? Give at least two values in terms of λ.
(b) For what values of δx will the superposition of the two waves show total destructive interference? Give at least two values in terms of λ.

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Based on our data, we think this problem is relevant for Professor Arratia Munoz's class at UCR.