This visualisation shows two travelling sinusoidal waves on separate tracks and the wave you get when they are added together underneath. The key idea is that interference is not a separate process happening afterward — it comes directly from adding the displacements of the two waves at each position in space. You can drag the purple probe line to pick one x-position and compare the values there. The coloured markers show the displacement of Wave 1, Wave 2, and the combined wave at exactly the same location. The readout below makes the addition explicit, so you can see how a positive and a negative displacement may partially cancel, while two displacements with the same sign reinforce each other. Use the play/pause button to freeze the motion when you want to inspect a particular moment carefully. As the waves move, notice that the lower wave continually changes because the sum is recalculated point by point across the whole screen. That is the essence of interference: wave heights add locally, everywhere. This visualisation shows two identical sinusoidal waves that stay perfectly in phase. That means each crest lines up with a crest and each trough lines up with a trough. Because both waves point in the same direction at the same positions, their displacements add together instead of cancelling. You can move the amplitude slider to change the height of both source waves at once. Notice that the red resulting wave updates immediately and always becomes twice as tall as either single wave. This is constructive interference: matching phases produce reinforcement, so the sum has greater amplitude. Use the animation button to pause and inspect the alignment, or let the waves move to see that the relationship stays true over time. Watch the dashed guide and the amplitude marker on the right to connect the idea of “same direction displacement” with the visibly larger resulting wave. This visualisation shows two sinusoidal waves being added point by point. Wave A stays fixed, while Wave B can be shifted in phase with the slider. The bottom track shows the combined result, so you can see interference happen directly rather than just reading about it. When the phase shift reaches **180°**, the two waves are half a cycle out of phase. That means every crest of one wave lines up with a trough of the other. If their amplitudes are equal, the positive displacement from one is matched by the negative displacement from the other, and the result becomes a flat line: **destructive interference**. You can drag the **phase shift slider** to move Wave B toward or away from exact opposition. Use the **amplitude slider** to keep both waves at the same size while watching the result track shrink as the phase approaches half a cycle. Notice how the green combined wave is largest when the waves reinforce and smallest when they cancel. This visualisation shows two sinusoidal waves and the wave you get when you add them point by point. The blue wave stays fixed, while the pink wave is shifted by a phase difference. The green wave is their sum, so its amplitude changes depending on how well the two input waves line up. Drag the pink handle on the phase dial to change the angular offset continuously. When the phase difference is near 0°, crests align with crests and troughs align with troughs, so the sum becomes large: this is strong constructive interference. When the phase difference moves toward 180°, high points line up with low points, so the sum shrinks toward cancellation. Notice that the change is smooth, not all-or-nothing. Intermediate phase differences produce partial reinforcement or partial cancellation, which means interference depends continuously on alignment. You can also hover over the marked points to identify crests and troughs and compare how their positions shift as the phase changes. This visualisation shows two coherent wave sources sending out circular ripples across a water-like surface. Every point on the plane feels both waves at once, so the color represents the combined displacement there: blue regions are positive displacement, red regions are negative displacement, and pale areas are close to zero. You can drag either source to change the spacing and orientation of the interference pattern, and use the wavelength slider to change how far apart the ripples are. Notice how the bands of strong disturbance and weak disturbance shift immediately. That happens because the path difference from the two sources changes from place to place. The blue example marker highlights a constructive point, where the waves arrive in step so peaks meet peaks and troughs meet troughs. The red example marker highlights a destructive point, where a peak from one source meets a trough from the other, cancelling the disturbance. Watch how those locations move as you manipulate the sources: the whole interference map is controlled by geometry and wavelength. This sandbox shows the superposition principle in action. Each incoming wave has its own amplitude, wavelength, and phase, and the green curve is always the sum of the blue and orange displacements at each horizontal position. That means interference is not a separate rule — constructive and destructive interference are just special cases of adding wave values point by point. You can move any slider and see the combined wave update immediately. Try matching the amplitudes and wavelengths, then change the phase to watch the result shift from reinforcement to cancellation. When crests meet crests, the green wave grows larger; when crests meet troughs, the green wave shrinks or can nearly disappear. Use the reset button to return to a strong cancellation example, then experiment from there. Notice that even when the total pattern looks complicated, the rule stays simple: at every point, add the displacement from the left wave to the displacement from the right wave.