destructive interference

Meaning: When waves overlap, their displacements add (superposition). If a crest meets a trough, the net displacement is smaller than either wave alone. Cancellation is complete only when the amplitudes are equal and the waves are 180° (π rad) out of phase. The waves then continue unchanged, and the energy is redistributed to places of constructive interference rather than lost.

Equation: Δr = (m + ½)λ, where Δr is the path difference from the two sources to the point (m), λ is the wavelength (m), and m = 0, 1, 2, ... is an integer. This holds for sources emitting in phase. Equivalently, the phase difference is Δφ = (2m + 1)π, in radians.

On the MCAT: Typical setups are the double-slit experiment (dark fringes), two speakers producing quiet spots, noise-cancelling headphones, thin films, and nodes of standing waves. You are given a path difference and a wavelength and asked whether the point is loud or quiet, bright or dark. If the wavelength changes, you predict how the fringe positions shift.

Common confusion: Students think the energy is destroyed. It is not; it is redistributed. Another mistake is using whole-number wavelengths for destructive interference. For in-phase sources, whole numbers give constructive interference. If the sources are 180° out of phase, the conditions swap.