Re: Midterm Question - Sort of

[Leigh Palmer <palmer@SFU.CA>]

James McLean wrote:

> 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.

The deletia here obscure the fact that the second "No" in this quote
follows and answers a rhetorical question, not the question you asked.

> 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.

You are certainly free to think that, but in my opinion it is an *ad
hoc* construction. You really know what resonance is, and you wish to
store this particular phenomenon into your bag of phenomena labelled
in that way. I argue that it is not useful to do so, and I adduced
your undergraduate physics experience as an example of the improper
conception which might be conveyed.

> 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.

I do not wish to consider the bowing of a violin as a resonance
phenomenon, but it decidedly fits in the same category as the TNB
oscillation.

> 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?

I don't think the Q of the bridge was much greater than ten*. The
vortex shedding was in sync with the motion of the bridge, but over
an appreciable range of wind velocities. The feedback was perfect;
the moving bridge formed its own vortices, not the von Karmann type
seen with a stationary obstacle. The vortices shed by the fipple
are examples of the latter type, but they are synced with pressure
oscillations in the tube (strong feedback). Still, only a limited
range of airflow velocities will excite a given note.

Leigh

*You're going to want to know what my definition of Q is. I'm not
putting in the factor of 2 pi. Q here means that the energy of
the oscillation would diminish by 1/Q per cycle, not per radian.
Ten is just a hazily remembered number anyway. In this case it
corresponds to a 5% decrease in amplitude on successive
oscillations.