Nikon D3100 produces sound when I take the photograph. The sound is loud and attention grabbing.
What is the term for this particular sound, and how can I turn it off?
Just use the Quiet Drive mode on your D3100. It is marked by a Q.
What you hear is the Mirror-Slap and cannot be removed completely unless you change to a mirrorless camera which are extremely quiet. The Nikon 1 J1 for example is ultra-quiet because it does not have a mechanical shutter either, which is the other noise the D3100 does.
To use the Quiet mode, press the shutter has you take the shot and it will do so more slowly than usual. Then, release it slowly, maybe a few seconds later when there is more ambient noise. This reduced the noise from the mirror since it moves slower.
There's two* sounds on the D3100 - the mirror slap sound and the beep.
The mirror slap occurs when the mirror flips up and down to reveal the sensor rather than redirect the light to the viewfinder. This happens in various degrees in all SLRs.
The beep is an electronic beep that confirms focus. You can disable this in the menus.
The D3100 does not have a common feature called 'mirror lock up' which will rotate the mirror up to take a picture without the mirror moving more. It has 'mirror lock up' listed in the menu, but its strictly a cleaning feature, you cannot take a picture while its active.
Live view on the D3100 doesn't solve this slap either. The camera still flips the mirror around when it takes the picture.
The D3100 does have one feature to help with it. The drive switch on the top right of the camera has a Q on the bottom. This will divide the sound into two stages. Up when you press the button, back down when you release - it makes it appear less noticeable in situations when you need it.
If the noise is a issue for you, this is an advantage of the breed of mirrorless cameras like the Olympus PEN or Sony NEX. There's no mirror, so there's no mirror slap.
The term is mirror slap. Essentially this is the noise made by the mirror flipping out of the way to allow the image to hit the sensor rather than be visible through the viewfinder.
Another disadvantage to the mirror slap is the added vibration from this action. It can introduce unwanted movement to the camera, and cause issues in long-exposure images.
You can use the mirror lock or live view function of most current DSLRs to avoid this sound, and movement. You also could switch to a mirrorless camera such as a Micro-Four-Thirds camera.
In this Youtube video, you can see comparisons of many current Canon DSLRs mirror slaps. I would say that the 5D MK II is the quietest of the bunch. Although it is not a direct comparison, or necessarily fair, this is an example of the Nikon D3100.