Understand wave superposition and interference

This wave superposition simulation helps you predict the resultant displacement when waves overlap. Pause the animation, compare the individual waves at the same position, and check your prediction against the resultant.

Add displacement, not amplitude alone

The principle of superposition states that the resultant displacement is the algebraic sum of the individual displacements: y = y₁ + y₂. For example, a displacement of +3 cm overlapping a displacement of −2 cm produces +1 cm. The signs describe opposite directions from equilibrium.

Constructive and destructive interference

Displacements in the same direction reinforce; displacements in opposite directions partially or completely cancel. Equal waves in phase have a resultant amplitude twice that of either wave. Equal waves in antiphase can cancel completely. Cancellation of displacement does not mean that energy has simply disappeared.

Try a prediction before pressing play

Compare equal and unequal wave heights. Predict where the resultant will be zero and where its displacement will be greatest. When two travelling pulses overlap in a linear medium, they then continue through one another; the resultant during overlap is not a permanent new pulse.

Build on this with standing-wave and other physics simulations, then apply the principle to A-Level waves and optics questions. Superposition underpins interference, diffraction and standing waves.