It is found empirically that as long as the amplitudes of waves in most media are small, two waves in the same physical location don't interact with each other. Thus, for example, two waves moving in the opposite direction simply pass through each other without their shapes or amplitudes being changed. When superimposed, the total wave displacement is just the sum of the displacements of the individual waves. This is called the superposition principle .
Interference is a consequence of the superposition principle.
When two or more waves are superimposed, the net wave displacement is just the algebraic sum of the displacements of the individual waves. Since these displacements can be positive or negative, the net displacement can either be greater or less than the individual wave displacements. The former case is called constructive interference , while the latter is called destructive interference . Let us see what happens when we superimpose two sine waves with different wavenumbers. Figure 1.5 shows the superposition of two waves with wavenumbers and .