Houjun Liu

Rossing 1990

On the dynamics of Tuning Forks. (Rossing, Russell, and Brown 1992)

Characterizing Tuning Forks

Aluminum, tines 10mm apart. Four main groups of vibration:

  1. Symmetrical In-Plane
  2. Antisymmetrical In-Plane
  3. Symmetrical Out-Of-Plane
  4. Antisymmetrical Out-Of-Plane

(a) and (c) are in the first group; (b) is in the second group, where the fork just warps.

Deriving Tuning Forks’ Frequency

As per before, we can treat tuning forks acting in clang and fundamental modes as a good’ol fashioned cantilever beam.

The frequency action of a cantilever beam is defined as follows:

Otherwise, for asymmetric modes, we can use the same exact expression but with uniform rods unfixed at either end:

Note that density is not uniform at this point (because the bottom handle-y bit.)