Re: [Phys-l] neat video of synchronizing metronomes

[John Denker <jsd@av8n.com>]

On 07/21/2011 09:48 AM, Brian Blais wrote:

> Interesting synchronization of metronomes.  

> http://www.youtube.com/watch?v=W1TMZASCR-I&feature=player_embedded#at=54

Here's a better link to the same video:
  http://www.youtube.com/watch?v=W1TMZASCR-I

The latter starts at the beginning, before synchronization has
occurred.  It also makes more clear the structure of the apparatus, 
including the roller bearings underneath the board.

> Any good physics lessons here?  Perhaps some lab activity?

Interesting question.  See below (*) for philosophical and 
pedagogical issues ... but first, some physics:

Coupled oscillators are relevant to all sorts of physics ... 
including subatomic physics and cosmology and more-or-less 
everything in between.  This is a topic that needs to be 
introduced early and then touched on again and again and again.

At the introductory level, you can get some insight into what's
going on in terms of linear transformations, change of variables,
and normal modes.

... skip ...

The physics of pianos is endlessly interesting.  The relevant 
bit here is the fact that most notes have /three/ strings per
note.  Three coupled oscillators ... *not* quite tuned alike.

... skip ...

Phonons are the normal modes of an N-particle solid.  This is
kinda important.  Manifestations include:
 -- the simple existence of sound waves
 -- the simple dispersion relation of ordinary sound waves
 -- the not-so-simple dispersion relation for ultrasound
 -- the Debye / Einstein heat capacity
 -- the Mößbauer effect

--- skip ...

At a more advanced level, this has to do with perturbation theory,
which most people learn about in the context of quantum mechanics
(Fermi's golden rule etc.) but was understood for eons before that 
in classical mechanics.  Buzzwords include "resonant denominator".

This has many manifestation throughout physics.  Spectroscopy
provides some familiar examples.  Buzzwords include "avoided
crossing".  The hyperfine structure of atoms can be considered 
an example;  see item 5 of:
  http://free-ideas.org/p210/a/2010/s09/

The structure of the rings of Saturn, including the famous gaps
in the rings, is another interesting example.  This was not
really understood until the Voyager missions.  I remember the
looks on the faces of the scientists ... they were like kids
in a candy store.

Other issues of orbital resonant stability and instability
have been known since the late 1600s.

The effect (as seen in the metronomes, and elsewhere) is slower 
and larger than you might think -- i.e. lesser in the short run 
and greater in the long run -- to a degree that relates to the 
Q of the resonances.

   This is a metaphor for a proverb about politics and 
   life in general:  People tend to overestimate short-term
   change and underestimate long-term change.

A good pendulum clock has a much higher Q than an ordinary
metronome.  You can hang cuckoo clocks on the walls in
different rooms, even rather far apart in a large house,
and they will phase lock, assuming you tune things properly, 
and assuming the clocks are well made.  It's kinda spectacular 
to hear the cuckoos /precisely/ in synchrony, hour after hour, 
day after day.

==================

(*) Philosophical and pedagogical digression:  In the introductory
class, one faces a judgment call here.  When introducing this
topic, if you don't mention the applications and ramifications, 
students will have no idea why the topic is important.   OTOH if 
you say too much about the applications and ramifications, some
of them will get confused and/or intimidated.