Question

what will occur when the trough of wave a overlaps the crest of wave b?
destructive interference will occur, causing the new wave to have more energy than wave a or wave b.
constructive interference will occur, causing the new wave to have more energy than wave a or wave b.
destructive interference will occur, causing the new wave to have less energy than wave a or wave b.
constructive interference will occur, causing the new wave to have less energy than wave a or wave b.

Explanation:

When the trough of one wave overlaps the crest of another wave, destructive interference occurs. In destructive interference, the waves cancel each other out to some extent. Since energy of a wave is related to its amplitude (higher amplitude means more energy), when trough (negative amplitude part) and crest (positive amplitude part) overlap, the resultant amplitude (and thus energy) of the new wave is less than the amplitudes (and energies) of the individual waves (Wave A and Wave B).

Answer:

Destructive interference will occur, causing the new wave to have less energy than Wave A or Wave B.