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Re: [Phys-L] types of mechanical waves

On 05/31/2014 09:11 AM, Bill Nettles wrote:

I believe it is important that these students, AT THE LEAST, realize
there are different modes and they affect real structures in
different ways: a longitudinal wave in a thin I-beam will have a
effect different from a transverse wave in the same beam which in
turn will differ from the effect of a torsional wave, and a vibration
source touching that beam will produce all three modes.

That's fine. I think it's better to talk about different
/modes/ and different /polarizations/ (rather than different
"kinds" or "types" of waves, as the Subject: line might
suggest). That was the main point of my previous note.

Concrete is very strong under compressive forces but very weak under
shear. Longitudinal waves would affect concrete very differently
than transverse waves.

I wouldn't have said that.

In fact, concrete is strong under compression and weak
under /extension/. Note that pushing (strong) and pulling
(weak) are both /longitudinal/. Bringing shear into the
picture seems like a red herring.

As an extreme example of the basic idea, visualize a pile of
gravel. It strongly resists compression, but it comes apart
if you pull on it. That's why nontrivial concrete construction
uses prestressed /reinforced/ concrete. Steel bars strongly
resist extension, but crumple under lengthwise compression.
The combination of concrete + rebar is a tremendous win.

As another extreme example, sonoluminescence uses transverse
waves to pull apart the water. There are no shear waves

Also, there is a huge difference between /strength/ (as in
yield strength) versus elastic modulus.
-- Wave speed depends on the modulus, in ordinary conditions.
-- Unless the wave is extraordinarily intense (e.g. earthquake
or sonoluminescence) it is not going to cause the material
to yield.

Bottom line: There is not the slightest reason to expect that
a transverse wave affects concrete worse than a longitudinal
wave. Actually, other things (such as intensity) being equal,
a longitudinal wave is probably /more/ effective at pulling
apart unreinforced concrete.

In the introductory course, sound is usually studied in the
linear regime. Mechanical failure is exceeeedingly nonlinear.
In the introductory course, I would vehemently recommend
keeping failure modes separate from wave propagation, at
least at first. If you are going to study yield and failure
at all, start with /static/ loads, not waves.

So, I'm concluding that the important content for an introductory
cal-based course, regarding modes of wave motion is there are 3
primary modes of mechanical wave propagation: transverse,
longitudinal, and torsional.

The "importance" depends on the situation:
-- For a thin wire, there are no relevant torsional modes.
-- For a long thick bar or hollow drive shaft, there is
some moment of inertia per unit length, and torsion modes
become possible.
-- For a big chunk of solid, there are modes in the bulk,
plus surface acoustic waves.
-- For a crystal with a polyatomic unit cell, there are
all kinds of complicated modes.
-- Et cetera. See previous note.

You are free to decide that torsion modes are "important"
to you but SAW modes are not ... or vice versa ... but
please keep in mind that that's a personal choice, not a
law of physics.

In particular, maybe the mechanical engineering students
are interested in torsional modes ... but meanwhile maybe
the chemistry students are more interested in vibrational
modes of complicated molecules. It's a choice, not a law
of physics.


While we are on the topic of different "kinds" of "wave",
somebody should mention /shocks/. (Experts tend to call
'em /shocks/ rather than "shock waves".) It is fairly
easy to demonstrate a shock, using a falling slinky. Here
is a video. It's better if you turn off the sound, because
the explanations are complete nonsense, but the video gives
a reasonably clear view of the phenomenon:

If you want a clear correct description of what's going
on, look here:
W. G. Unruh
"The Falling Slinky"

The details are beyond the scope of the introductory
course, but IMHO this is not as far out as yield and
failure, and not nearly as far out as conflating yield
and failure with basic wave polarization and propagation.

My priority would be something like this:
1, 2, 3, and 4: Basic waves.
5: Modes and polarizations.
6: Waves with a nontrivial dispersion relation, such
as water surface waves, or EM waves in a waveguide.
7: Nonlinear waves and solitons.
8: Shocks.
9: Cavitation, sonoluminescence, yield, and failure.