I was playing around with modeling wave forms with OpenSCAD and ended up creating a series of physical representations of wave interference.
The image above shows the first model I made. It demonstrates the interference patterns that occur over time when two waves of equal magnitude, but out of sync meet while traveling in opposite directions. Here is a 2-d version of the same pattern:
With the two wave out of sync, there is a point (shown by the red dot) where complete destructive interference occurs. If these were sound waves, a microphone positioned at the red dot would not pick up any sound. If they were light waves, that point would be dark.
I also sliced and printed the model for two color printing to use color to highlight the point in space where no movement occurs:
The next model I created shows the same two waves moving towards each other, but one of them is shifted so that they are in sync when the meet. Under these conditions the crests and troughs add to each other and constructive interference occurs at the point where the two waves meet.
The two color version of this model has the red line highlighting the point in space where the maximum amount of constructive interference occurs:
There are some interesting symmetries between space and time under these two conditions. When the two waves are in sync, there is one point in time where the surface of the model is completely flat and one point in space where maximum displacement occurs.The opposite is true when the waves meet out of phase: There is one point in space where no displacement occurs and maximum displacement occurs at one point in time.
In fact, I didn’t really need to create two different models. With the parameters used to create these surfaces, switching axes changes the relationship between space and time. That is, rotating either model 90 degrees, turns it into the other model.
The single color stl files are available for viewing and download from github: