Wave interference

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

For interference in radio communications, see Interference (communication).

Etymology[edit]

The word interference is derived from the Latin words inter which means "between" and fere which means "hit or strike", and was used in the context of wave superposition by Thomas Young in 1801.^[1]^[2]^[3]

Constructive interference: If the phase difference is an even multiple of $π$ : $\varphi =\ldots ,-4\pi ,-2\pi ,0,2\pi ,4\pi ,\ldots$ then $\left|\cos(\varphi /2)\right|=1$ , so the sum of the two waves is a wave with twice the amplitude $W_{1}+W_{2}=2A\cos(kx-\omega t)$

Destructive interference: If the phase difference is an odd multiple of $π$ : $\varphi =\ldots ,-3\pi ,\,-\pi ,\,\pi ,\,3\pi ,\,5\pi ,\ldots$ then $\cos(\varphi /2)=0\,$ , so the sum of the two waves is zero $W_{1}+W_{2}=0$