Re: Midterm Question - Sort of

[James McLean <jmclean@CHEM.UCSD.EDU>]

Leigh Palmer wrote:
> > > It always bothers me when the Tacoma Narrows Bridge collapse is
> > > cited as an example of resonance.  The wind was steady, more or
> > > less, and there was no significant component at the bridge's
> > > resonant frequency.
> > Huh?  Isn't this precisely the reason that it *is* an example of
> > resonance?  Because of a high Q, the extremely small driving force at
> > the resonant frequency was able to drive a large amplitude oscillation.
>
> No, I don't believe that is relevant. <deletia>
> No, the mechanism must have its own
> positive feedback mechanism to keep the force in the proper phase.
While your detailed explanation of the periodic wind turbulence is
certainly more than I had considered, I think the crucial difference
between our viewpoints is in the choice of system.  I was considering
only the oscillating object (the bridge) and the force applied to the
object (by the wind).  The complex turbulence mechanism by which the
steady wind produces an oscillating force is outside of my system.
Within that system, I think resonance is really what is going on.

When there is significant positive feedback from the oscillator to the
forcing agent, this choice of system is a pretty poor way to look at
things.  Certainly this is the case in most musical instruments:  the
trumpet feeds back to the player's lips, the opening and closing of a
reed feeds back to the wind forcing it, and the violin string motion
feeds back to the stick-slip of the bow.  In these cases, one is forced
to consider the larger, more complicated system.

But is there a big feedback in the case of the TN Bridge?  My vague
recollection is that the turbulent vortices leave the object pretty
regularly, even if the object is immobile.  Does the frequency (and
phase coherence) of the vortex departure really depend on the motion of
the bridge?  What about in the case of an organ pipe or recorder (the
wind instrument) fipple?

--
--James McLean
jmclean@chem.ucsd.edu
post doc, UC San Diego, Chemistry
moving to SUNY Geneseo Physics this fall