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Two waves shown below with the same amplitude, A, and wavelength, lambda, and traveling in the same direction Initially the sources (dot at the origin) are also at the same point

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Two waves shown below with the same amplitude, A, and wavelength, lambda, 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 delta x. a) For what values of ox will the superposition of the two waves show total constructive interference? Give at least two values in terms of lambda. b) For what values of delta x will the superposition of the two waves show total destructive interference? Give at least two values in terms of lambda.

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When two waves travelling superimpose on one another,

constructive interference will be formed when the phase difference i.e., angular separation between the wave is either zero or 180⁰

To convert phase difference into path difference, the following relation is used.

i.e., phase difference = 2*pi/ $\lambda$ (Path difference)

So Path difference = $\lambda$ /2*pi (Phase difference)

i.e., Path difference = $\lambda$ /2*pi (0) =0

(or) = [ $\lambda$ /2*pi ](pi) = $\lambda$ /2

Thus, interference takes place when the path difference is zero (or) $\lambda$ /2

a) Constructive interference is formed when the path difference is an integral multiple of $\lambda$ ,

i.e., dx = 0, $\lambda$ , 2 $\lambda$ , 3 $\lambda$ ,...,n $\lambda$

In this crest of one wave falls on the crest of another wave, so bright fringe is formed.

b) Destructive interference is formed when the path difference is an integral multiple of $\lambda$ /2,

i.e., dx = 0, $\lambda$ /2, 3 $\lambda$ /2, 5 $\lambda$ /2,...,n $\lambda$ /2

In this crest of one wave falls on the trough of another wave, so dark fringe is formed.

Two waves shown below with the same amplitude, A, and wavelength, lambda, and traveling in the same direction Initially the sources (dot at the origin) are also at the same point

Physics