A tuning fork is a tool for producing vibrations at a particular frequency. Usually made out of metal, consisting of a base and two prongs. The vibrations it produces have a variety of applications.

In use, the tuning fork is held by the base and the prongs struck sharply on something (wood is ideal) or twanged with the fingers. The bottom of the base is then rested firmly against a solid surface. This has the effect of forcing the fork into a single vibrational mode, and ensuring that it produces a clear and exact note. As an unexpected side effect, the volume also seems to increase.

Here's a diagram of a tuning fork:

               _     _
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             || |  || |
             || |  || |
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             ||  `-'  |
             \\       /
              \\     /
               \\___/
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                \|_|


The way the tuning fork vibrates can be modeled by considering just the tips of the prongs, as points vibrating in a 2D plane. There are four possible vibrational modes. Imagine looking down on the fork (tilting the top of the diagram above 90 degrees towards you, out of the screen:)

      ______\      /______           |  __            ^
        __  /      \ __              | |__|          /|\
       |__|         |__|             |                |
                                     |                |
                                    \|/           __  |
       /______   ______\             V           |__| |
       \   __     __   /
          |__|   |__|

            mode 1.                       mode 2.


     /______   /______               ^                ^
     \  __     \  __                /|\ __        __ /|\
       |__|      |__|                | |__|      |__| |
                                     |                |
                                    \|/              \|/
         ______\    ______\          V                V 
           __  /     __   /
          |__|      |__|

             mode 3.                       mode 4.

In modes one and three, the prong tips move laterally; always in opposite directions in mode 1, always in equal directions in mode 3.

Similarly, in modes two and four, where the movement is "vertical" (well, orthogonal to the plane common to the base and both tips when at rest ...) the prongs move always in equal directions in mode 4, always opposite in mode 2.

When the prongs are randomly struck, they will vibrate in random combinations of these modes, and the multiple vibrations will tend to cancel each other out.

But notice: mode 1 is the only mode in which the resultant of the movements of the tips is zero: not only are the tips always moving oppositely, their movements always have the same magnitude at any given time. So this mode does not create a movement in the whole tuning fork. In all the other modes, adding up the movements of the tips gives a non-zero result - the movements tend to induce a movement in the fork. Mode 2 induces a rotation, mode 3 induces swaying from side to side, mode 4 induces a vertical wobble.

So when the base of the fork is damped, modes 2, 3 and 4 are damped too, but mode 1 is not affected. All the vibrational energy starts operating in mode 1. This is why the note clears and gets louder.


Info from: http://www.phy.hw.ac.uk/~peckham/matrices/eigenvalue/tuning_fork/tf.html

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