16.10:
Interference and Superposition of Waves
When two waves are physically present in the same location, the resultant disturbance is a third wave. This effect is called interference.
Mathematically, interference can be described by the principle of superposition. It states that if two or more waves overlap at the same point, the resultant wave is the algebraic sum of the individual waves.
While taking the algebraic sum, both the amplitude and phase need to be considered.
When two waves superpose at a point with the same phase, the resultant wave has an amplitude equal to the sum of the individual wave's amplitudes. This phenomenon is called constructive interference.
On the other hand, when two waves superpose at a point with opposite phases, the resultant wave's amplitude is equal to the difference between the two individual waves' amplitudes. This phenomenon is called destructive interference.
When constructive and destructive interference occur in alternate regions, we get an interference pattern.
16.10:
Interference and Superposition of Waves
When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence, interference implies that the physical displacement of a medium's particles is given by the algebraic sum of the displacements that the individual waves cause. Interference also occurs in other waves like electromagnetic waves, in which case the electric and magnetic fields add up vectorially.
However, the principle of superposition does not apply to certain waves. That is, the resultant wave may not be a simple algebraic sum of the individual waves. In this case, the effect is nonlinear, complicating the description of the phenomenon. These waves are said to be nonlinear waves.
Alternative bands of constructive and destructive interference may result in interference patterns, a smoking gun signature of wave phenomenon occurring in nature.
This text is adapted from Openstax, University Physics Volume 1, Section 16.5: Interference of Waves.