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Re: Tuning Forks



On 04/11/2003 11:51 AM, Roger Haar wrote:

Here at the U of Arizona, in our junior-senior
lab, we have the students make tuning forks as an
introduction to machining metal. We measure the
fork's frequency when it is complete, with an
amplified microphone and a frequency counter. This
is quite popular activity.

But there are several questions about tuning
forks that come up:

1. Physically, how is the tuning fork bending in
its fundamental and harmonics?

This is quite an interesting question. I was
wondering about it a few weeks ago. The odd
thing is that if you build a tuning fork the
way people think they are built, and use it
the way people think they are used, it won't
work at all.

Typically you whack the fork and then hold the
stem against a sounding-board, or against your
cheek bone. But if the fork were symmetric,
as you might think it should be, the handle
connects to a node, and there should be no
coupling to the fundamental.

The trick is to make it not quite symmetric.
The amount of asymmetry controls the coupling
coefficient. You want it to be small but
nonzero.

The mode of interest is the obvious one, the
flapping mode: stretch out your arms above
your head and clap.


2. What is the theoretical resonant frequency or
how to design a tuning fork for a desired
frequency?

It's the usual physics of bending a beam.


3. Many of our tuning forks including several
commercially made tuning forks resonate on 5th
(or maybe 4th) harmonic. Often this harmonic is
much stronger than the fundamental, but usually
this harmonic decays faster than the fundamental
so we can eventually get a good measurement.
Is there a method of exciting a tuning fork to
avoid harmonics?

-- Don't whack it at the end of the tines. That
couples at least as well to the high harmonics as
to the fundamental.
-- There are several good reasons for not whacking
it with something hard.
-- Best of all, drive it on resonance with a weak
excitation at roughly the right frequency. An
electromagnetic or piezo driver (and a laboratory
signal generator) will do nicely.

You can then map out the amplitude AND PHASE of
the response function. If you were trying to
build a clock using the tuning fork as the
timekeeper (and some fine clocks have been
made this way) you would find the phase response
to be much more useful than the amplitude.