The simultaneous progress of more than one wave through a region of space produces the phenomenon known as the superposition of waves. During superposition, each of the waves travels independently, a wave retains its individual properties though it overlaps on other waves.
If more than one waves are incident simultaneously on a particle in a medium, the particle would have different displacements for each of the separate waves. But these displacements of the particles occur at the same time. A resultant displacement of the particle occurs for all the waves. Since displacement is a vector quantity, the resultant displacement is the vector sum of all the individual displacements. This is known as the principle of superposition of waves.
Statement:
The resultant displacement of a particle in a medium due to more than one wave is equal to the vector sum of different displacements produced by the individual waves separately.