Superposition
Add two waves and watch them reinforce or cancel
From superposition, standing waves, beats and the Doppler effect to interference, diffraction, refraction and thin films — 12 wave simulations you can touch and explore.

Three categories: wave basics, sound waves, and waves in a plane & light. Drag and slide to see the waves change instantly.
Add two waves and watch them reinforce or cancel
Reflection at a fixed or free end
Harmonics on a string: count the nodes
Build square and triangle waves from sines
Two close pitches make a beat
A moving source squeezes the waves ahead
Resonance in closed and open pipes
Tap the water to make ripples
Fringes from two point sources
Waves bending through a slit
Waves bending at a boundary (Snell's law)
Why soap films and oil slicks shine in color
Tap the water, drag a sound source or move a slider and the waves respond in real time.







Tap the water to make ripples, drag the source and observer, and change frequency and amplitude with sliders.
Every screen has a hint on how to try it, plus the physics and formulas behind it.
Dark and light themes, large text, landscape and tablets are all supported.
English, Japanese, Chinese (Simplified / Traditional), Korean, Spanish, Portuguese, German, French and more.
The app is free. There are no in-app purchases, subscriptions or paid unlocks.
A Pangle banner ad is shown at the bottom of the screen. On iOS, the App Tracking Transparency (ATT) prompt appears at launch, and ads are personalized only if you allow tracking. On Android, the app asks once whether ads may be personalized. Either choice can be changed later from "About this app" > "Ad settings".
Requirements: iPhone and iPad with iOS 15.0 or later; Android 7.0 (API 24) or later phones and tablets.