# Static vs. Dynamic Representations

I was reading through a colleague’s homework questions about interference and came across a question asking whether two nearby light sources, each emitting monochromatic light but of different frequencies, could produce an interference pattern. The answer key said ‘no’ but I spent quite a bit of time arguing with myself that the answer should be ‘yes’. Why was I so confused? It had to do with the way I was thinking about the problem.

I started by trying to construct a double slit diagram like we do when deriving equations for bright and dark spots. I pulled out a sheet of paper and sketched the following diagram:

Clearly there are points on the screen where light from each slit is arriving in phase despite their different frequencies. I made another sketch showing a point where the waves arrive in phase on the other side of the center line. I was now fairly convinced that the answer key was wrong and that there would be an interference pattern. The pattern would be asymmetric with bright spots closer together on one side of the center line than the other but I was certain the interference pattern would exist.

I decided to look online for a simulation simulation and came across this one that was well suited for my question. The simulation shows bright and dark spots sliding along the screen rather than staying place. This finally got me thinking dynamically. Yes, at the moment in time shown in my sketch the two waves arrive in phase at that point on the screen. But these waves are dynamic. They’re waving. A moment later their different frequencies will cause the waves to be out of phase at that point on the screen.

My thinking about interference patterns is so tightly coupled to the representation above that I couldn’t conceptualize the question dynamically until seeing a dynamic representation. I’m used to thinking about the limitations of two-dimensional representations of three dimensional scenarios but I probably need to spend more time thinking about the limitations of static representations of dynamic scenarios. I also need to look for places where my understanding of a concept is primarily dependent on a single representation.

Thanks for this, it’s exactly the type of thing I like to think about to push myself. I didn’t fall for the same mistake you made because my view of this problem is tied to the dynamic simulations I use when teaching this. However, I think I do make mistakes like this with other problems, and reading this nudges me to think about representations when I’m tackling a new idea.