Interference is the physical phenomenon that occurs when two or more waves occupy the same region of space and interact so that their resulting disturbance is determined by the combination of their individual disturbances. The principle applies to many kinds of waves, including sound waves, water waves, light waves, radio waves, seismic waves and waves associated with quantum particles. For linear waves, the relevant mathematical principle is superposition, which states that when waves overlap, their instantaneous displacements add algebraically.
If two disturbances have the same sign at a particular location and time, the combined disturbance can become larger, producing constructive interference. If they have opposite signs, they can partially or completely cancel, producing destructive interference. Interference therefore does not normally mean that waves collide and permanently alter one another. Instead, overlapping waves pass through the same region while their disturbances combine temporarily, and after separation each wave continues according to the properties of its medium or propagation environment.
Constructive interference occurs when corresponding parts of waves arrive with a suitable phase relationship so that their amplitudes reinforce one another. For two sinusoidal waves of the same frequency travelling through the same region, maximum constructive interference occurs when their phase difference is an integer multiple of a complete cycle. Destructive interference occurs when the waves are approximately half a cycle out of phase, so a crest of one wave coincides with a trough of the other.
Complete cancellation is possible when two waves have equal amplitudes, identical relevant waveform characteristics and exactly opposite phase at the point being considered. Partial cancellation is more common because amplitudes, phases, frequencies and propagation conditions are rarely perfectly matched. Interference can therefore produce alternating regions of strong and weak disturbance rather than simply making a wave permanently stronger or weaker.
Phase is central to understanding interference. The phase of a periodic wave describes where the wave is within its repeating cycle, while phase difference describes the relative positions of two oscillations. A path difference can create a phase difference because waves travelling different distances generally arrive at a point at different stages of their cycles.
For monochromatic waves in a uniform medium, a path difference of one wavelength corresponds to a phase difference of one complete cycle and therefore produces constructive interference, while a path difference of half a wavelength produces destructive interference under the appropriate conditions. More generally, interference depends on the complete phase relationship, not merely on physical distance. Changes in wavelength, frequency, propagation speed, source position, reflection conditions and medium properties can all alter that relationship and therefore alter the observed interference pattern.
Interference is particularly important for light because visible light is a wave and can produce stable interference patterns when suitable sources are coherent. Youngs double slit experiment provides a classic demonstration. Light passing through two closely spaced slits produces overlapping waves on a screen, creating alternating bright and dark regions. Bright fringes correspond to constructive interference and dark fringes correspond to destructive interference.
The experiment demonstrates wave behaviour because the pattern cannot be adequately explained by treating light only as independent classical particles travelling along separate paths. Similar principles appear in thin film interference, where light reflected from different surfaces of a very thin layer can interfere. Depending on wavelength, thickness, viewing angle and phase changes upon reflection, some wavelengths are reinforced while others are suppressed, producing colours such as those seen in soap bubbles and oil films.
Sound interference occurs when sound waves overlap in air or another medium. Two loudspeakers emitting sound of the same frequency can create locations where the sound is louder and other locations where it is quieter because the waves arrive with different phases. This is one reason sound levels can vary significantly over relatively short distances in some environments.
Interference also underlies active noise control, in which a system generates a sound wave designed to have an approximately opposite phase to unwanted sound at a target location. The unwanted and generated waves then interfere destructively, reducing the resulting pressure variation. Effective cancellation depends on frequency, timing, spatial position and system response, so cancellation is generally strongest within the intended region rather than everywhere simultaneously.
Interference can be classified according to whether the interacting waves maintain a sufficiently stable phase relationship. Coherent waves have a predictable phase relationship over the relevant observation period and are capable of producing stable interference patterns. Incoherent sources have rapidly varying relative phase, so their interference pattern generally averages out when observed over an appropriate time.
Ordinary independent light bulbs, for example, do not normally produce a stable large scale interference pattern because their emissions are not mutually coherent in the required sense. Lasers can provide highly coherent light, making them particularly useful for interferometry. Coherence can involve temporal and spatial properties, and practical coherence is always limited. A source with a broad range of frequencies can lose a stable phase relationship over longer time intervals, while an extended source can lack sufficient spatial coherence for clearly resolved interference fringes.
Interference has important applications in measurement and technology. Optical interferometers use interference to detect extremely small changes in distance, refractive index, frequency or phase. Interferometric methods have been used for precision measurements of wavelengths, surfaces and astronomical phenomena, and gravitational wave detectors use laser interferometry to detect extraordinarily small changes in the relative lengths of long optical paths.
Radio astronomy also uses interference between signals received by separated antennas to obtain information with an effective angular resolution associated with a much larger observing baseline. In acoustics, interference influences architectural sound fields, loudspeaker design and noise control. In engineering, interference can be beneficial when it is deliberately exploited, or undesirable when it creates unwanted signal cancellation, electromagnetic coupling or measurement artefacts.
Interference should not be confused with diffraction, reflection or refraction, although these phenomena can be closely connected. Diffraction describes the spreading and redistribution of waves when they encounter apertures, obstacles or edges, and the resulting pattern often contains interference because different parts of a wave can reach the same region by different paths. Reflection changes the propagation direction at a boundary, and reflected waves can subsequently interfere with incident or other reflected waves.
Refraction changes propagation direction because wave speed changes between media, and waves emerging from different regions can also develop phase differences. In quantum mechanics, interference has an especially important interpretation because probability amplitudes can interfere, with measurable probabilities depending on the squared magnitude of the combined amplitude. Thus interference is a broad wave phenomenon whose underlying principle is superposition, while its observable form depends strongly on the type of wave, coherence, geometry, boundary conditions and measurement arrangement.
