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Re: [Phys-L] types of mechanical waves

your note was the stimulus for me to reflect on the production and transmission of waves in media. I can easily see the axial compression traveling wave, and the axial standing or resonant compression wave. I can visualize the torsional traveling wave and the torsional standing or resonant wave.
I visualize the transverse traveling and the standing waves which could have two modes on transverse axes. That's eight types so far, but I am fairly sure I haven't populated all the possible entities. I am not sure it makes entire sense to talk about the speed of standing waves - whose essence is to vary but not to travel, but for the traveling waves, I see no strong reason why their speeds would not differ.

Brian Whatcott Altus OK Indian Territory.

On 5/31/2014 11:11 AM, Bill Nettles wrote:
I know the details are complicated, but I didn't ask for the details you gave me. I asked whether a torsional mode is a distinct mode compared to transverse and longitudinal. Even in your discussion you mention that the speeds of the modes are very different. That could be important, e.g., in analyzing seismic data. I've even built a wind chime tube in which there was resonance between the transverse waves in the metal and the air column (the sound goes on for-almost-ever).

Of importance regarding the modes (how the medium moves compared to the disturbance propagation throughout the medium) is knowing how those modes affect the medium. I teach a lot of (pre-)engineers, and they will eventually have to deal with waves and vibrations of structures. Different materials have different responses to different wave modes. Concrete is very strong under compressive forces but very weak under shear. Longitudinal waves would affect concrete very differently than transverse waves. 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.

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. Actual waves are very complicated and can be sums of these three modes as well as sums of many frequencies of simple harmonic waves. Understanding the basic properties of wave motion (amplitude/intensity, period/frequency, wavelength, wave speed) apply to all these modes, but the speeds of each mode, even in a common structure will differ, and the strength of the material of the structure will differ for each mode.
-----Original Message-----
From: Phys-l [] On Behalf Of John Denker
Sent: Friday, May 30, 2014 6:19 PM
Subject: Re: [Phys-L] types of mechanical waves

On 05/30/2014 03:14 PM, Bill Nettles wrote:
Working on content for the fall semester. When it comes to
mechanical waves, the general consensus is there are at least two
important types based on disturbance vs propagation directions:
transverse and longitudinal. Some sources mention "surface waves"
but this seems to me to be a combination of transverse and
longitudinal and not a distinct type.

I've also seen the term axial wave. Is that yet another type or not?
1) The details are complicated.

2) OTOH I'm not sure the details are important. Even if
the distinctions are correct, I'm not sure the distinctions
are worth emphasizing.

The alternative is to de-emphasize the distinctions and
adopt the view "if you've seen one wave you've seen 'em all."

In particular, consider the Wilberforce machine
wherein the torsional mode is coupled to the up-and-down mode.

In general, you have to write /one/ equation that covers
both modes. After an artfully-chosen change of variables
you can achieve a separation of variables, but the new
/normal modes/ will be different from the /basis modes/ that
you started with. Each basis mode was either torsional or
up-and-down, but the normal modes will be mixtures.

3) I see it mainly as a question of /polarization/.

3a) For electromagnetism, there are two transverse polarizations.
In a calcite crystal, you can tell them apart, because they
travel at different speeds.

To my mind, the fact that electromagnetism has transverse
components is not nearly so interesting as the fact that the
longitudinal component is missing. Actually it's not even
entirely missing! The Coulomb interaction is longitudinal.
It is mediated by the exchange of longitudinally-polarized
/virtual/ photons.

3b) In a solid, such as in the crust of the earth,
you see both transverse waves and longitudinal waves.
These are polarizations. The geophysicists call these
s-waves and p-waves respectively (short for shear-waves
and pressure-waves). They travel at different speeds.
I don't see this as different "kinds" of waves so much
as different polarizations with different speeds, sorta
like calcite.

3c) A piano string does have a longitudinal mode. Its
wave speed is very high compared to the transverse modes.
Note that the "gong" inside a cuckoo-clock is made of
a spiral coil of piano wire. The sound comes from
longitudinally polarized resonances in the wire.

For nominally-transverse waves on a piano string, the
excitation is truly transverse only to a first approximation,
for small amplitudes. For large amplitudes and/or if you
look more closely, the motion is complicated ... almost as
complicated as the "rolling" motion of a wave on the surface
of the ocean.

This doesn't change the terminology. That is OK, given
that the so-called transverse waves are still "mostly"

3d) In a multicomponent system, such as a plasma, or a crystal
with a polyatomic unit cell (such as salt or sugar), there
can be all sorts of vibrational modes. These are sometimes
classified in various ways, such as "acoustic branch" and
"optical branch". To visualize the optical branch, imagine
a sound wave in NaCl where all the Na atoms are moving one
way and all the Cl atoms are moving the other, 180 degrees
out of phase.

3e) In solids we also have surface acoustic waves, which
are different from the waves in the bulk (the aforementioned
s-waves and p-waves).

3f) A coil spring blurs the distinction between longitudinal
and transverse. Overall stretching of the spring corresponds
to bending the wire of which the spring is made. OTOH you
can still have a truly longitudinal wave that runs along
the wire, around and around, at very high speed.

4) As an alternative to asking "what is the polarization" you
could ask "what is the ordinate of the wavefunction". Mostly
this comes to the same thing. It is particularly relevant to
quantum mechanics, where the ordinate is a complex number.

Also along this line, there are such things as spin waves,
where the ordinate is the orientation of a spin vector.
Visualize a wave of falling dominoes. Also visualize a
lattice of compass needles, where if you wiggle one needle
the others respond.

Another: a torsional wave
Yes, same idea.

seems to me to be a distinct type.
I'm still not sure the distinction is important. It's still
just a wave, and if you've seen one wave you've seem 'em all.
This is just another choice of ordinate for the wavefunction.

I mention again the Wilberforce machine, where the torsional
mode is coupled to the up-and-down mode.
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