Looking at the bridges of string instruments, especially the baroque ones, seems to me the best way to start looking at what happens to mechanical waves in an instrument.  The baroque models are designed to let waves reach the front of the instrument by the short way, while modern bridges are quite the opposite. The shapes of those bridges are so clear, with all their different elements, you really get surprised of how smart those designs are, each one for its kind of instrument... 
I need to say that to fully understand the shape of a bridge you need yourself to play the instrument good enough to be able to feel under your bow the differences between one shape of bridge and another or, if you don't, having somebody who does to tell you what she or he feels. However, by looking at the different models bearing in mind how mechanical waves propagate you get a pretty good idea of what happens in each of them. Let's start!

In the next pictures you see a baroque model of bridge for cello. In the left one are represented the waves coming from the point where a string aproximately would lie on this bridge. In all directions, as long as no surfaces are encountered, that's why the rings: they are the addition of all the waves' trajectories in all directions. In the picture at the right are represented a few of those trajectories and you can see how those waves rebound when encountering the surfaces of the bridge. You'll see too that some of the waves coming from that string reach the ground of the right foot undisturbed, in a direct stright line. 

If you look at the modern bridge in the next picture, always bearing in mind mechanical wave propagation, you'll see that the heart is actually in the way of the waves to the feet of the bridge. In consequence, and opposite to the baroque bridge for cello, where a lot of the waves coming from the inner strings reach the ground of the feet directly, in this modern violin bridge you won't find a single one that does reach the feet of the bridge.