EngineerHub.orgWhat this simulator teaches
Interference is not a separate force or interaction: it is the result of adding wave displacements at the same place and time. These six views connect the same mathematics to traveling waves, coherent sources, double-slit fringes, standing waves and beats.
superpositionphasepath differencecoherencenodesdouble slitstanding wavesbeats
Select interference model6 animated learning modes
Wave controls
Superposition
Two coherent traveling waves1D superposition — waves add point by point
Wave 1 and Wave 2 are shown separately above their instantaneous sum. Change relative phase to move continuously between reinforcement and cancellation.
y = y₁ + y₂
Wave 1Wave 2ResultantNode / reference
Four ideas that explain interference
01 / Linear superpositionAt each point, the resultant displacement is the algebraic sum of all contributing wave displacements.
02 / Phase differenceEqual-frequency waves reinforce when their phase difference is near 0° and cancel when it approaches 180°.
03 / Path differenceA path difference Δr creates a phase difference 2πΔr/λ. Geometry therefore turns wavelength into spatial fringes and nodal lines.
04 / CoherenceStable interference patterns require a stable phase relationship. If relative phase wanders rapidly, fringes average away.
Model assumptions & limits
The simulator uses ideal sinusoidal, linear waves. It is intended to reveal cause and effect, not replace detailed acoustics, optics, structural dynamics or CFD.
Where intensity is shown, the model uses the standard proportionality I ∝ A². Values are normalized unless an absolute scale is explicitly stated.
The two-point-source view intentionally uses equal geometric amplitude across the plane so the interference geometry is easy to see. Real water, acoustic and electromagnetic waves may spread and attenuate with distance.
The double-slit screen pattern uses a Fraunhofer far-field interference model with a finite-slit diffraction envelope. It is most accurate when the screen distance is large compared with the Fresnel scale (roughly L ≫ a²/λ) and observation angles are modest. The tool also keeps slit width below slit separation so the two openings remain distinct.
The standing-wave mode assumes an ideal string fixed at both ends, so allowed wavelengths are λₙ = 2L/n and nodes occur at the boundaries.
Background & FAQ
In a linear medium, yes. During overlap their displacements add, but after passing through one another each wave continues according to the medium's wave equation. Interference describes the overlap, not permanent annihilation.
Local displacement can cancel, but energy is redistributed rather than destroyed. In spatial interference patterns, low-intensity regions are accompanied by higher-intensity regions elsewhere.
Adjacent maxima differ in path by one wavelength. For small angles, fringe spacing is approximately Δy = λL/d, so larger λ or screen distance L increases spacing, while larger slit separation d decreases it.
A standing wave is the sum of two equal waves traveling in opposite directions. At node positions the two contributions remain equal and opposite at every instant, so the displacement is always zero there.
Two nearby frequencies alternately move into and out of phase. Their phase difference advances at the difference frequency, so the amplitude envelope repeats |f₁ − f₂| times per second.
No. Linear superposition and interference appear in water waves, sound, electromagnetic waves, vibrating strings, structural vibration and quantum wave amplitudes, although the physical quantity represented by the wave differs.