Re: Energy visibly flowing

["John S. Denker" <jsd@MONMOUTH.COM>]

At 06:48 PM 9/21/01 -0700, Simon Lorimer wrote:

> Turning the water on at one end of the 20 meter pipe caused water to come
> out of the end practically at the same instant, though clearly the flow of
> water takes much longer.

OK.  Interesting example.

> I wonder if I can say that some energy has flowed along the pipe

Sure.

> I assume at the speed of sound in the water.

Probably mostly yes, but see below....

Undoubtedly *some* energy flowed at the speed of sound in water.  The
*sound* of water rushing into one end could be heard at the other end very,
very soon after.  The speed of sound in water is very high.

If the pipe in question is made of metal, the speed of sound in iron and
steel is even higher than the speed of sound in water, and some sound may
have propagated at that higher speed.

However, sound waves are not the only waves that can propagate in
water.  Suppose we repeat the experiment using ordinary plastic garden
hose, instead of steel pipe.  Then there will be complex interactions
between the water pressure and the elastic properties of the hose.  You
wind up with bulge in the hose that propagates faster than the
unconstrained waves you see on the surface of the ocean, but slower than
the canonical speed of sound in the bulk liquid.

This bulge question does not arise for ordinary sound propagating in the
bulk liquid, for the following reason:  Consider a plane-wave sound
propagating in the x direction.  Compare it with a long straight hose in
the x direction.  The plane wave is like a WHOLE BUNCH of hoses all right
next to each other, none of which can bulge because each is constrained by
its neighbors.

> Here is a circumstance where there are 2 distinct 'flows'. Am I correct in
> calling both 'flows'?

Sure.

An even more interesting combination of flows occurs when you suddenly
partially occlude the downstream end of the pipe.  A pressure-wave
propagates upstream.  The water is flowing in one direction with one speed,
while the wave moves in the other direction with a radically different speed.

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

Other good examples of energy visibly flowing include the following:

The ordinary waves on a piano string are (to an excellent approximation)
purely transverse.  If you pluck the string at one end, a pulse travels to
the other end.  The energy of the pulse flows along with the pulse.  The
atoms of the string do not.  You can sent pulse after pulse all day,
transferring more and more energy, but at the end of the day all the atoms
of the string will be (to an excellent approximation) right where they started.

For a classroom demonstration you can use transverse waves on a rope.
        Note: It works better with high quality rope.  Get some nice
        Dacron kernmantel from the boat store; rope is cheap and lasts
        forever, so there is no point in fooling with junky rope.
Anyway, suspend a long arc across the front of the classroom, not too
tight.  Whack it near one end with a broomstick or some
such.  Result:  nice propagating pulse.  Clearly transverse.

To those who hesitate to call energy a "thing":  What about this transverse
wave-pulse?  It has a shape, which is preserved as the wave runs along.  Is
it a thing?  Of course it's a thing.  An incorporeal thing, perhaps, but a
thing nonetheless.  Look up the definition of "thing".  The wave-pulse has
different properties from the medium, and cannot exist without the medium,
but it has a reality of its own.  If you tie the rope to a chain (with
suitably matched impedance) the wave will propagate from rope to
chain.  The properties of the wave are preserved, while the properties of
the medium have changed.

A masochistic reductionist solipsist might argue that there is no such
thing as a wave;  all we have is a bunch of rope-molecules that conspire to
make you think there is a wave.  That makes about as much sense as saying
there is no chair under me, it is just a bunch of metal and polymers that
conspires to make me think it's a chair.  Well, it looks like a chair, I'm
going to call it a chair, and I'm going to continue sitting on it.

And what about energy?  To me, energy is more real than waves, and even
more real than chairs.  Most of the waves we deal with are quite
ephemeral.  Chairs are sturdier;  they are conserved (or nearly so) by a
wide class of low-energy interactions, but we know they can be destroyed
and they can be created from scratch.  Energy is very strictly conserved,
which makes it very, very special.