What's the role and the physics behind a sound box? I'm interested in the manufacturing of violins.
I was wondering what the role of the sounding box?
Why would it be worse if there were just a sound board?
Does the box just have to redirect the wave to the top of the instrument? So, it would also work with a box out of concrete (but I think it wouldn't).
Why does the box also have to vibrate, but not just the board and the air inside the box?
Thank you !
 A: The sound box couples the vibration of the instrument to the air around it, so that it makes more noise that a vibrating string would alone. The string alone displaces very little air, and so makes very little sound. The much larger surface area of the body means that it can displace much more air, and thus make much more sound when it vibrates.
The material the body is made out of is very important, as it must be light and thin enough to vibrate well, but also strong enough to not give out under the tension of the strings.
You can see essentially this effect by considering an acoustic violin (which has a sound box) to an electric violin (which does not). An electric violin has a solid body, which does not vibrate much and so does not produce much sound, and so requires external amplification.
A: Though it's true that the larger surface area improves the efficiency of the transfer of acoustical energy from the string to the air, there's another good reason for why a violin has the form of a box instead of a board.
The box and it's sound holes behave as a Helmholtz Resonator. This means that unlike a board, the box has a narrowband resonance frequency. 
A page devoted to violins on the same website provides an empirical spectrum for the violin, which shows that it has a strong resonant frequency near 300 Hz. The author of the webpage explains the plot like this:

This is the ratio of the sound pressure produced (recorded by a microphone near the f hole) to force applied (electromagnetically at the bridge).


So we can see that because of the body design of the instrument, notes near 300 Hz need much less physical force to radiate the same amount of acoustical energy.  It should be no surprise that the design of the body matches the range of the instrument:  300 Hz is in the center of the first two octaves of the violin's range (G3 to G5.)
