Question

what will occur when the trough of wave a overlaps the trough 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:

1. Recall the concepts of wave interference:

• Constructive interference occurs when two waves (either two crests or two troughs) overlap. In this case, the amplitudes add up, resulting in a wave with a larger amplitude.
• Destructive interference occurs when a crest of one wave overlaps a trough of another wave, and their amplitudes subtract, resulting in a wave with a smaller amplitude (or even zero amplitude in case of complete destructive interference).
• The energy of a wave is related to the square of its amplitude (\(E \propto A^{2}\)). So, if the amplitude increases (as in constructive interference with two troughs overlapping), the energy of the resultant wave will be more than the energy of the individual waves.

1. Analyze the options:

• Option 1: Says destructive interference, which is incorrect because two troughs overlapping is constructive, not destructive. Also, destructive interference would not result in more energy.
• Option 2: Constructive interference occurs when two troughs (or two crests) overlap. The resultant wave has a larger amplitude, and since energy is proportional to the square of amplitude, it has more energy than the individual waves. This matches the correct concept.
• Option 3: Destructive interference is incorrect here, and it also says less energy which is wrong for the situation of two troughs overlapping.
• Option 4: Constructive interference is correctly identified, but it says less energy which is wrong because a larger amplitude (from constructive interference) means more energy.

Answer:

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