For the topic of this blog post, I made a simulation to demonstrate how the sound insulation properties of building facades can be thought of. Take note that there are some instabilities which I didn't resolve, so running the simulation for too long might jam up your browser. Click the simulation to start it, and again to stop it.
Once again, you'll have the best experience with Chrome.
In the simulation, the sound source (represented by a red dot) will emit sound every once in a while. The sound is represented by the small colored dots in the simulation. The color of each dot represents the part of the facade the sound traveled through.
The room is quite deep, 15 meters (almost 50 feet), and the simulation spans 0.8 seconds.
Each time the simulation restarts, the insulation properties of one of the colored parts of the facade is worse than the others. Take a look to see how this affects things.
There are a multitude of things at play in the real world. When measuring the insulation properties of a facade, for example, the response of the room is taken into account by "correcting" the result (this involves, among other things, multiple measurement points and measurements of the reverberation in the room).
Predictive calculation methods used by consultants are usually statistical, which in practice leaves lots of details out of the situation. In most cases, though, a statistical approach is enough. The data available for doing the calculations is usually also limited, which makes the statistical approach a very viable option.
Something similar to the method presented here could in theory give better results in cases where the statistical approach isn't that viable of an option. I'm not sure about the simplification of sound traveling "straight through" the wall, though, as the situation is really more complicated than that (even though I know that some commercial software use this approach to model sound insulation).