Partially constructive / destructive interference

Meaning: Overlapping waves add by superposition: their displacements sum point by point. Fully constructive interference occurs when the waves are in phase (path difference 0, λ, 2λ, ...), giving the largest amplitude. Fully destructive interference occurs when they are exactly out of phase (path difference λ/2, 3λ/2, ...), giving the smallest amplitude, zero if the two amplitudes are equal. Any other phase difference gives partial interference, with a resultant amplitude between those extremes. Closer to in phase is partially constructive; closer to out of phase is partially destructive.

Equation: Anet = 2A|cos(φ/2)|, with φ = 2πΔx/λ. A is the amplitude of each of two equal waves and Anet is the resultant amplitude (same unit, such as m for a string wave); φ is the phase difference (rad), Δx the path difference (m), and λ the wavelength (m).

On the MCAT: A passage places two speakers or two slits and gives a detector's path difference in wavelengths. Classify the point as constructive, destructive or partial, then compare loudness or brightness. Intensity is proportional to amplitude squared.

Common confusion: Students treat every overlap as fully constructive or fully destructive. Those occur only at path differences of exactly nλ or (n + ½)λ; a path difference of λ/4, for example, is partial. Destructive interference does not destroy energy either; it redistributes it to other locations.