Hitting a string of a violin or a guitar will cause that string to vibrate, but after short time the amplitude of the vibration will decay, consequently the produced sound will die out.
I suppose this decay happens because of friction with air. If this is true then how much longer will the string keep vibrating in a vacuumed room? Any way to estimate this? Are there other effects that cause the damping?
Best Answer
The instrument is designed to make sound. The loss of energy is not due to friction, but to emitting sound. In a vacuum, a suspended plucked guitar would ring for minutes, not seconds.
EDIT: More detail
The loss of energy to sound is a direct mode-coupling, and it takes energy away regardless of internal friction. But you can estimate the degree to which internal friction is important by comparing the ringing time of materials with negligible internal friction for sound propagation--- crystalline materials like metals--- vs. complex polymers like wood or plastic, where the propagation of sound leads to losses because the restoring forces are partially entropic.
For a steel body guitar with steel strings, there is no plausible avenue for sound modes to decay fast in the resonator, because the steel is a crystal material. To get an estimate for internal losses in wood, compare the resonating time for a note/chord steel body guitar and a wood guitar in air. The wood guitar frictional losses are estimated by the decay time of the tone in a wood guitar vs. steel body.
Here is a steel body demonstration: http://www.youtube.com/watch?v=tVx62GpWKOE
I don't hear noticably less decay in the metal, so I assume that internal losses in wood are small compared to radiated sound energy.