Constructive interference occurs when two waves have displacements of the same sign when they overlap. Which statement describes the resulting displacement?

Constructive interference occurs when two waves have displacements of the same sign when they overlap. Which statement describes the resulting displacement?

• A. The resultant displacement is zero.
• B. The resultant displacement has a greater magnitude than either original wave.
• C. The resultant displacement is the average of the displacements.
• D. The waves do not interfere.

Answer: (B)

When two waves overlap, their displacements add at each point where they meet. If the two displacements have the same sign, they reinforce each other, so the instantaneous resultant displacement is the sum y = y1 + y2. Because both contributions add in the same direction, the resulting displacement has a larger magnitude than either one alone. For example, if both waves push in the same direction with amplitudes A and B, the overlapping region reaches A + B in magnitude, which is bigger than A or B individually. This is the essence of constructive interference: in-phase displacements combine to produce a bigger peak. Destructive interference would give a zero or reduced resultant displacement when the signs oppose, and the idea that the waves do not interfere contradicts the fact that their displacements do add or subtract wherever they overlap.

When two waves overlap, their displacements add at each point where they meet. If the two displacements have the same sign, they reinforce each other, so the instantaneous resultant displacement is the sum y = y1 + y2. Because both contributions add in the same direction, the resulting displacement has a larger magnitude than either one alone. For example, if both waves push in the same direction with amplitudes A and B, the overlapping region reaches A + B in magnitude, which is bigger than A or B individually. This is the essence of constructive interference: in-phase displacements combine to produce a bigger peak.

Destructive interference would give a zero or reduced resultant displacement when the signs oppose, and the idea that the waves do not interfere contradicts the fact that their displacements do add or subtract wherever they overlap.