Surface waves in water showing water ripples
The interference of two waves. When in phase, the two lower waves create constructive interference (left), resulting in a wave of greater amplitude. When 180° out of phase, they create destructive interference (right).
Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.
Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave
Wavelength λ, can be measured between any two corresponding points on a waveform
Interference of waves from two point sources.
Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)
A magnified image of a coloured interference pattern in a soap film. The "black holes" are areas of almost total destructive interference (antiphase).
Sine, square, triangle and sawtooth waveforms.
Geometrical arrangement for two plane wave interference
Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.
Interference fringes in overlapping plane waves
Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.
Optical interference between two point sources that have different wavelengths and separations of sources.
The red square moves with the phase velocity, while the green circles propagate with the group velocity
Creation of interference fringes by an optical flat on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface.  The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the bottom plate undergoes a 180° phase reversal.  As a result, at locations (a) where the path difference is an odd multiple of λ/2, the waves reinforce.   At locations (b) where the path difference is an even multiple of λ/2 the waves cancel.  Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands, interference fringes, are seen.
A wave with the group and phase velocities going in different directions
White light interference in a soap bubble. The iridescence is due to thin-film interference.
Standing wave. The red dots represent the wave nodes
The Very Large Array, an interferometric array formed from many smaller telescopes, like many larger radio telescopes.
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
Schematic of light being dispersed by a prism. Click to see animation.
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Formation of a shock wave by a plane.
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A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.
Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles
One-dimensional standing waves; the fundamental mode and the first 5 overtones.
A two-dimensional standing wave on a disk; this is the fundamental mode.
A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude.

- Wave interference

This phenomenon arises as a result of interference between two waves traveling in opposite directions.

- Wave
Surface waves in water showing water ripples

4 related topics

Alpha

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The brighter areas represent a higher probability of finding the electron.

Quantum mechanics

Fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

Fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.

Wave functions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations. The brighter areas represent a higher probability of finding the electron.
Fig. 1
Position space probability density of a Gaussian wave packet moving in one dimension in free space.
1-dimensional potential energy box (or infinite potential well)
Some trajectories of a harmonic oscillator (i.e. a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H). In quantum mechanics, the position of the ball is represented by a wave (called the wave function), with the real part shown in blue and the imaginary part shown in red. Some of the trajectories (such as C, D, E, and F) are standing waves (or "stationary states"). Each standing-wave frequency is proportional to a possible energy level of the oscillator. This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.
Schematic of a Mach–Zehnder interferometer.
Max Planck is considered the father of the quantum theory.
The 1927 Solvay Conference in Brussels was the fifth world physics conference.

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave–particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).

Another consequence of the mathematical rules of quantum mechanics is the phenomenon of quantum interference, which is often illustrated with the double-slit experiment.

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

Wavelength

Spatial period of a periodic wave—the distance over which the wave's shape repeats.

Spatial period of a periodic wave—the distance over which the wave's shape repeats.

The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.
Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)
Wavelength is decreased in a medium with slower propagation.
Refraction: upon entering a medium where its speed is lower, the wave changes direction.
Separation of colors by a prism (click for animation)
Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore
A sinusoidal wave travelling in a nonuniform medium, with loss
A wave on a line of atoms can be interpreted according to a variety of wavelengths.
Near-periodic waves over shallow water
Wavelength of a periodic but non-sinusoidal waveform.
A propagating wave packet
Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.
Diffraction pattern of a double slit has a single-slit envelope.
Relationship between wavelength, angular wavelength, and other wave properties.

The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Sinusoids are the simplest traveling wave solutions, and more complex solutions can be built up by superposition.

Crest and trough in a wave

Crest and trough

Crest and trough in a wave

A crest point on a wave is the maximum value of upward displacement within a cycle.

When the crests and troughs of two sine waves of equal amplitude and frequency intersect or collide, while being in phase with each other, the result is called constructive interference and the magnitudes double (above and below the line).

Superposition of almost plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.

Superposition principle

Sum of the responses that would have been caused by each stimulus individually.

Sum of the responses that would have been caused by each stimulus individually.

Superposition of almost plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.
Rolling motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: translation without rotation, and rotation without translation.
Two waves traveling in opposite directions across the same medium combine linearly. In this animation, both waves have the same wavelength and the sum of amplitudes results in a standing wave.
two waves permeate without influencing each other
green wave traverse to the right while blue wave traverse left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves.

Fourier analysis is particularly common for waves.

The phenomenon of interference between waves is based on this idea.