Principle of superposition
Principle of superposition: for waves of the same frequency meeting at a point, the resultant displacement is the algebraic sum of the separate displacements there.
When waves meet, their displacements combine. For equal-amplitude waves of the same frequency, the two limiting cases are constructive interference and destructive interference.
Constructive interference
If the waves meet in phase, their crests and troughs coincide.
Their displacements add, so two equal-amplitude waves produce a resultant with twice the amplitude of either wave.
Destructive interference
If the waves meet in antiphase, a crest of one corresponds to a trough of the other.
For equal amplitudes, the opposite displacements cancel and the resultant displacement is zero.
The same displacement-adding rule is used for transverse and longitudinal waves, whether the resulting behaviour is progressive or stationary.