As a kid I was bemused at why soundboards worked. A small sound could be demonstrably amplified simply by attaching the source to a surface that is rigid and not too thick. How could the volume increase so much given that there was no extra energy added?
As an adult I kind-of-think I know, but there are still many nagging questions. I assume it has to do with the waves propogating from a vibrating object actually being a compression on one side of the object just as they are a decompression on the other side, and something about that lack of coherence limits the volume. Exactly why remains a mystery to me. Is separating the pocket of compression and decompression so that the boundary along which they meet is quite small part of the issue?
My question is what are the physics that make a soundboard work?
Interesting specifics that would be nice-to-knows would be why does a hollow one (like a violin) work better than a solid one (imagine a filled in violin)? How important are the harmonics of the solid? But the real question is what are the physics that make a soundboard work?
P.S. I am a mathematician, so feel free to wax very mathematical if it is necessary to give a good explanation.
Best Answer
The comments above that say the sound is louder because the soundboard itself begins to vibrate are correct. This is called resonance. It sounds louder because the motion of the board is mechanically more efficient at converting the energy of the system into sound waves than the string alone. The board is an effective radiator of sound energy. A louder sound wave has a larger amplitude.
If you want a mathematical analysis that shows resonance, try the ODE for a one dimensional SHO being driven by sine function. You'll see the amplitude of your oscillator increases near the natural resonance period of the system. You could also do a 2D analysis on a thin plate such as a drum head.
Strings and thin plates are relatively good sound radiators because relatively low force is required to cause a larger displacement, and so a sound wave of larger amplitude.