Re: core material for gobo?


"Chris Hornbeck" <chrishornbeckremovethis@xxxxxxx> wrote in message
news:28duu3ldnprhb847lemv5d06qde0ult3pv@xxxxxxxxxx
On Sun, 30 Mar 2008 01:19:13 -0400, "Soundhaspriority"
<nowhere@xxxxxxxxxxx> wrote:

Can a dissipative structure somehow foreshorten the
physical limits of a plain-old-air-system acoustic
transformation?

You're thinking of a kind of a solid lens? The sound propagates from air
into a solid structure, through the equivalent of an antireflective
coating?
Once inside, the equivalent of optical glass (not dissipative) does
something to the sound, and spits it out the other side? There are some
uses of solids, such as speaker cones filled with some kind of material,
that I'm sure you're familiar with. But seems to me that the principle
obstacle is that the wavelength of sound is much larger than the
wavelength
of light. This limits practical lens-building.

Wasn't really thinking about acoustic lenses. There were
things with that name, back when I was in short pants, but
the name was mostly ficticious. As you say, wavelength
issues make the idea impractical.

But acoustic (impedance) *transformers* can be built with
the simple structure of waveguides that vary in area with
linear time. One end has high pressure-to-velocity
ratio; the other has the reciprocal.

My concern with any dissipative structure is in its
acoustical impedance presented to room air. Room air
is such a low impedance that coupling to and from it
is very difficult to and from ordinary mechanical
devices.

Loudspeakers see this problem from one end. They're
mostly high mechanical impedance devices trying to drive
the low acoustical impedance load of room air.

Room resonance damping devices see the problem from
the other direction. They'd like to be high impedance
devices in order to minimize their physical (acoustical)
"depth", but the high acoustical impedance would cause
reflections in their interface to room air, decreasing
their efficiency.


If so, will it revolutionize the design of acoustic
transformers (acoustic horns), or is the wavelength
foreshortening inextricably related to the turbulence?

Or, to put it another way, can we specify a device/structure
that looks to room air like more room air (and is minimally reactive)
yet is itself dissipative? And is orders of magnitude smaller than
the free-air-equivalent acoustic transformer structure?

Physics has lovely analogies. There are two that might help here. One
begins with two pucks on an air table. If the two pucks have identical mass,
the impactor transfer it's entire kinetic energy to the target. After the
collision, m2 continues to move with the same velocity as m1, now
stationary, had. This is equivalent to the interface between two materials
of equivalent acoustic impedance. The energy in material #1 is tranferred
entirely to material #2.

The other has to do with measuring the index of refraction of a piece of
optical glass. If the glass is highly polished, one could determine the
index of refraction simply by measuring the strength of the reflection of a
beam. This isn't done in practice, because measuring the angle of refraction
is easier and more accurate. But the nice thing about this situation is:
1. Glass is hard
2. The interface is shiny and well defined
3. We don't need to think about what's behind the interface, provided it
isn't a metal with free electrons, so there is no temptation to confusion
from mixing regimes.

The reason I mention this is that with a typical absorber, the interface is
not hard, shiny, and flat, so the problem can grow unnecessarily in one's
imagination. There are two physical viewpoints: one is macroscopic, as with
the glass, and the other is microscopic, with fibers and atoms dancing
around. But we don't want to mix the two. The bulk properties, the
impedance/dissipation, do not exist in the microscopic viewpoint.

So the easiest way to slice the problem up is to aim a sound wave at the
absorber, and the reflection will tell you what the equivalent bulk
properties are. If nothing comes out, then the interface (from the pov of
the wave) looks continuous with air. If it all comes back, the sound is
telling us that there is a sharp discontinuity at the interface. You can
measure this, correct a little for absorption per linear centimeter, and be
happy that you have determined the bulk properties "for that regime."

The bulk properties exist only to tell us what will happen at the interface.
The magic of absorption is a microscopic phenomenon, capsulized by a
dissipation coefficient. But capsulizing in a coefficient requires us to
look at the problem in a certain way, a "regime." The regime changes
depending upon who is looking at it:

1. Air (from the pov of a human or jetliner): modeled by Navier-Stokes, has
very low longitudinal and transverse viscosities, which are the dissipative
terms.
2. Air (from the pov of an insect) looks like a viscous fluid, because the
space/time scale is radically different.
3. Water: (from the pov of a human) similar to air from the insect view,
except water does not compress much.
4. Foam: (from the pov of a small intensity wave) looks like a fluid with
high viscosity coefficients.
5. Foam: (from the pov of a large intensity wave) looks like a rubbery
solid.
6. Air (from the pov of an atom) looks like a game of dodgeball. Knows
nothing about sound.
7. In between regimes: This is for mathematical amusement, as the terms
multiply, there are no laws, and little can be done. There are very
complicated calculations done by the liquid crystal people et al.

And so forth. The economical way to approach it is to figure out which
regime applies, and then jam the problem into that form, knowing that it is
a useful lie.

Bob Morein
(310) 237-6511



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