The pattern below is produced by interference between identical waves emitted by

Question

The pattern below is produced by interference between identical waves emitted by two sources. Red denotes positive displacement of the medium, while blue denotes negative displacement. Black indicates zero displacement. At the orange point near the top, we say that constructive interference is occurring. The distance the orange point is from the left source is the length of the purple line; the distance the orange point is from the right source is the length of the green line.

For constructive interference to occur at the orange point, the net displacement must be non-zero at all times at that point.

For constructive interference to occur at the orange point, the distance from each source to the orange point must be an integer number of wavelengths.

For constructive interference to occur at the orange point, the path-length difference for the orange point must be an integer number of wavelengths.

The path-length difference is the distance the point is from the left source minus the distance the point is from the right source.

In this particular case, the orange point is two wavelengths farther from the left source than it is from the right source.

(b) In this case, what is the distance between the two sources, in terms of wavelengths?
?   wavelengths

Explanation / Answer

Solution: We know that in case of constructive interference to occur, the condition is ?x = n?, where ?x = optical path difference between the two associated paths and ? = wavelength. Here, n is representing an integer. Therefore, true options from part a are:

For constructive interference to occur at the orange point, the path-length difference for the orange point must be an integer number of wavelengths.

The path-length difference is the distance the point is from the left source minus the distance the point is from the right source.

In this particular case, the orange point is two wavelengths farther from the left source than it is from the right source.

Part b: In this case, the distance between the two sources, in terms of wavelengths is = 9?.

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