If two waves of equal amplitude are perfectly out of phase, the resultant amplitude is:

• A. Zero
• B. Doubles
• C. The frequency becomes zero
• D. The wavelength doubles

Answer: (A)

Destructive interference cancels the wave’s motion when two waves of equal strength arrive exactly out of step. If their phases differ by 180 degrees, the peaks of one align with the troughs of the other, so their displacements add to zero at every point in time and space. Mathematically, two waves with equal amplitude A, one written as y1 = A sin(ωt) and the other as y2 = A sin(ωt + π) = −A sin(ωt), sum to y_total = A sin(ωt) + (−A sin(ωt)) = 0. So the resultant amplitude is zero. The frequency and wavelength of the individual waves aren’t changed by this cancellation—the waves simply cancel each other out when they superpose. In real situations, energy may be redistributed, but the instantaneous resultant displacement becomes zero due to complete destructive interference.