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Which of the following situations would result in constructive interference? Check all that apply.
A 1.77 cm crest intersecting with a 0.65 cm crest
A 1.2 mm crest intersecting with a 3.9 mm trough
A 4.55 N trough intersecting with a 1.59 N trough
A 0.44 inch trough intersecting with a 0.72 inch crest
A 7.42 mm trough intersecting with a 1.93 mm trough

Constructive interference is interference that occurs when two waves of the same frequency amplitude and wavelength travelling in the same direction are superposed with the resultant effect of reinforcement of both waves to produce a larger wave.

Constructive interference occurs when the path difference between two identical waves at a point is:

delta s = n × wavelength

where n = 0, 1, 2, ...

For the various intersections:

1.77 cm crest intersecting with a 0.65 cm crest; n = 1.77/0.65 = 2.7
A 1.2 mm crest intersecting with a 3.9 mm trough is destructive.
A 4.55 N trough intersecting with a 1.59 N trough; n = 4.55/1.59 = 2.8
A 0.44 inch trough intersecting with a 0.72 inch crest is destructive.
A 7.42 mm trough intersecting with a 1.93 mm trough; n = 7.42/1.93 = 3.8

Therefore, none of the wave intersections will produce constructive interference

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