[Phys-L] Re: water outflow (was earthquake)

[jsd at AV8N.COM (John Denker)]

John Barrer wrote:
> Eyewitness beach accounts described the water rapidly
> receding prior to the arrival of the first wave. This
> is also local lore in other places that have
> experienced tidal waves. What mechanism is responsible
> for this "outflow"?

There's a ton of physics here, and pedagogy, too.

The first pedagogical point is that typical textbooks spend far
too much time talking about monochromatic waves, at the expense
of polychromatic waves and pulses.  Of course they have to
start with the simplest case ... but they should not leave the
impression that they have described the general case.

For starters, the physics of waves propagating on the ocean
surface is dispersive.  So even if we simplify the wave as
starting out as a step function, it won't remain a step
function for long.  For big waves in deep water, it is the
long waves that run out ahead of the short waves.

   BTW for electromagnetic waves in a waveguide, it is the
   short waves that run out ahead of the long wave, hence the
   classic "whistlers" you can hear with an AM radio.
     http://www.google.com/search?q=ionosphere+whistler+dispersion

Secondly, propagation of spherical waves (or circular waves) is
dispersive, even in a medium that we think of as non-dispersive
in the sense that it would be non-dispersive for plane waves.
The derivative in polar coordinates has additional terms in it.

Having saved the best for last, let me say the same thing in
less-mathematical, more-physical terms:

Suppose you launch the wave by suddenly injecting more of the
medium-material at a point.  A familiar example is setting off
a firecracker, which suddenly injects additional gas.into the
atmosphere.  Now, as the wave propgates outward, it is subject
to *two* conservation laws: local conservation of energy, and
local conservation of material.  For radial propagation in
D>1 dimensions, you can't satisfy both requirements with a
step-function-shaped wave.  The amount of material in the step
is proportional to amplitude, while the energy in the step is
proportional to amplitude squared.  You can't have a step that
decays like 1/R^(D-1) and sqrt(1/R^(D-1))) simultaneously. The
energy law predicts a relatively slow decay of the amplitude.
The only way you can do that, without requiring additional
material, is for the energy to be contained in positive *and*
negative displacements.  The negatively-displaced pieces
make a positive contribution to the energy, but a negative
contribution to the amount of material.

This is why you can tell how far away an explosion is, just by
listening.  Up close, you perceive a sharp snap.  Far away, you
perceive a boom.

IMHO that's a really nifty example of qualitative reasoning.

This brings us to the second pedagogical point:

Remember, Galileo published a book _On Two New Sciences_.
One of those sciences was the laws of motion.  What was the
other one ... something that Galileo thought was more-or-less
just as important as the laws of motion?

I think a physics course is not worthy of the name if we just
teach the laws of motion and don't teach scaling laws and how
to use them.