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Old 11th August 2008, 05:23 PM   #21
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Location: Netherlands
Hi Calvin, MJ

The problem is that we don't have a working theory. So the only thing we can do is guess about the conditions for this effect to occur. So far we have:

a) the panel should be a strip source (todo: define ratio h/w)
b) it only applies for frequencies with a wavelength that is short compared to the height h (todo: define ratio h/labda)
c) the working distance of the effect depends on panel height (todo: define h/d)

h = panel height
w = panel width
d = panel to microphone distance
labda = source wavelength

I took the liberty of doing some measurements on a nearly flat strip source: w=3.5cm, h=59cm (the middle strip of a Quad ESL treble panel). The strip is flanked by two neighboring strips, undriven, one on each side, which could be a source of vestigal baffeling, but it could also be argued that those are for the better part acoustically transparant. The total width of the panel is 19cm. Total height 65cm. So there is some vestigal baffeling, but IMO it can still be considered a line source.

Frequency domain: 2kHz to 25kHz.

Distances varying between 1cm and 2m.
I hope we can all agree that this setup satisfies the conditions mentioned above. Here's the result:

Click the image to open in full size.

Distances going from top to bottom: 1cm, 2cm, 5cm, 10cm, 25cm, 50cm, 1m, 1.5m and 2m. Other conditions: 42% relative humidity, 25 degrees Celcius. Panel suspended in air, center 1 meter above ground. Microphone at straight angle with panel surface and aligned with the center of the panel (on a professional stand with no interfering objects nearby).

There is some interesting stuff in the graphs (most likely related to interference). But most relevant to the discussion is that on no occasion did the output rise at any frequency with increased distance, except for a small anomaly when going from 1cm to 2cm distance above 23kHz.
The results speak for themselves and the conclusion is that the effect can not be observed under these conditions, and certainly not over a wide distance and frequency range.

MJ: I concur, and I've also never seen anything in sound theory that can explain it. Constructive and destructive interference is well documented for flat and curved panels, and as far as I know does not show this 'max SPL at a distance' effect. Now stereo could be a whole different ball game.


I'm open to suggestions.

regards,
Arend-Jan
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Old 12th August 2008, 12:09 AM   #22
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Hello,
I bought a spray called Plasti-Dip today. I know brush application is better but the consistency was wrong and didn't have any solvents around. The spray covers well inside the holes. Its called Plasti-Dip has dielectric strength 1400V/mil, a spray on application 2-3mil thick while a brush 3-6mil thick. They also have something called liquid electric tape. This stuff is pretty easy to pick up, much cheaper and easier to get than Gylptal. I have 4 coats on one side of sample piece.

AJ
waiting for things to try... this effect is very intriguing. I can model what is going on by solving the pressure wave equation with Dirchilet boundary conditions. I will share the assumptions with you. If my assumptions are not too restrictive I will be able to predict on axis pressure in near and far zone. I will try to get this done ASAP, or maybe you have?
Bry
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Old 12th August 2008, 04:59 PM   #23
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AJ

I think what your hearing is constructive interference with the other speaker.


Can you repeat the experiment with one speaker off? I was confused because you said that you were on axis. If you have two on then you have to be off axis with respect to the other one. If on axis means perpendicular distance away from the source. If we still see the rise in SPL with just one on, then we have to try to limit the other variables, the room, the quads baffle etc.

Take Care
Bryan
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Old 12th August 2008, 05:39 PM   #24
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Hi Bryan,

Perhaps my post was not as clear as I hoped it would be. I'll clarify. It's a mono experiment (one panel) and it showed that SPL is decreasing with distance, which is the intuitive result e.g. what we experience in everyday life. The effect Calvin is talking about could not be demonstrated.

You mentioned modeling the wave equation. Do you have some special modeling software of are you talking about matlab or something similar? I always find modeling interesting so if you have something please tell us more about it.

Regarding the stator coating, I think you could do some flash testing if you have a step-up transformer. Just see if it holds or flashes thru the insulation. The usual cautions about high voltage apply etc.

regards,
Arend-Jan
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Old 12th August 2008, 08:43 PM   #25
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Hi AJ,

That sounds more intuitive, thanks for clarifying. Maybe to see the effect that Calvin mentioned we need to consider a stereo setup.

For testing the coating I was going to buy a cheap step-up transformer and wire the primary end to a speaker terminal on my amplifier. I do not have, nor what to buy a power-supply. When school is back in session I will have more access to a good oscilloscope. Do you think this is a safe idea? The transformer will probable be 50:1 and I will just earth ground the center tab.

I spent much time modeling ESL's. The model goes like this

The Electrostatic Part:

1. Determine the forcing on the membrane
a. we need to find the electric field everywhere in between the plates. There are three regions of interest between the plates, air, mylar, air. In all three regions the electric scalar potential obeys Laplaceís equation.
b. I assume that we coat both sides of the mylar with graphite. I looked around and some just coat one side. If we coat just one side then the uncoated side will develop an induced surface charge density that is about two orders of magnitude smaller than the free charge we can do put on with the power supply. This means that the forces (F=qE) on the left and right side of the film are not equal. It seems that we can get more forcing on the membrane if we just coat both sides.

b. I do not have access to a scanner right now, I will scan over the derivation tonight. I think my girlfriend does, or Iíll just use a digital camera.

Mechanical Part

1. With the force density known, we can solve the damped inhomogeneous (forced) wave equation with clamped edges (Dirchilet conditions). The initial conditions donít matter, since the membrane is forced. Right now I only care about the steady state solution (long time). However we do learn a lot about the performance by studying the transient part (we can send the speaker an impulsive voltage).
a. The solution to this partial differential equation will give us the amplitude response of the membrane.

b. It is important to consider the membrane damped since the air mass outweighs the membranes mass.


Acoustic Part
I only have the above two parts completed. Determining the pressure waves generated on axis is not to bad, off-axis things get a little hairy and may require numerical evaluation.


The software I like to use is mathematica, I used matlab for a little bit. Seems to me that mathematica is faster, has more options, can do almost anything, and has better user interface. I will use mathematica do write the simulation of all three parts.
Bryan
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Old 12th August 2008, 11:23 PM   #26
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AJ
This is the derivation to find the force density acting on the membrane. I donít have time now, but I will spell out the meaning of the parameters tomorrow and discuss the boundary conditions.

I saw your stretcher jig, looks like nice app of Newtonís laws. Any success using for curved panel?

Whoops file size is to big, let me get your email so I can send.
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Old 13th August 2008, 10:26 AM   #27
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Hi Bryan,

Wow, you've been busy! I have a lot of questions (at this point it's not completely to me clear what your approach is) but I'll wait for your e-mail and see what you have done before I start shooting.

The standard way to model the behaviour of a transducer is to make up an electro-mechanical model and translate the mechanical parts into electrical parts using a transduction coefficient. Then you can calculate or simulate the behaviour in the electrical domain, but only on a macro scale. It is however very usefull and you can use it to calculate frequency response on and off axis, input impedance and lot's of other usefull stuff.

Where a different approach could become really interesting is if you do not make the regular assumptions and simplifications, but instead simulate the actual physical process, e.g. the diaphragm has physical dimensions and distributed mass and charge, it is restricted in it's movement near the sides, acoustical coupling between regions, non-even air load and non-uniform electrical field because of stator holes and edge effects, diaphragm tension and resonance modes(!), etc, etc, etc.

I suppose the diaphragm could be simulated with a distributed spring-mass model and using finite element analysis. I have been fiddle-farting around with that some time ago but chickened out.

With a model like that you would move the desing of an ESL to a whole new level! It could be a ticket to your 15 minutes of fame. (it might require a super computer to do the sim though :-)

Okay, back to reality.
Some simple questions about your model that float around in my mind:
* do you model the diaphragm as constant voltage or constant charge? With constant charge (which is the better solution when it comes to ESLs), the electrical field would be pretty much Vsig/2d on a macro scale (the diaphragm would have to take on the potential of the electric field at that point).
* does your model incorporate the negative stiffness introduced by induced charge on the stators?

Quote:
If we coat just one side then the uncoated side will develop an induced surface charge density that is about two orders of magnitude smaller than the free charge we can do put on with the power supply.

This is an interesting topic by itself. How do you get to the induced surface charge of two orders of magnitude down? Is it something you simulated?

regards,
Arend-Jan
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Old 13th August 2008, 02:28 PM   #28
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I wrote:

With constant charge (which is the better solution when it comes to ESLs), the electrical field would be pretty much Vsig/2d on a macro scale (the diaphragm would have to take on the potential of the electric field at that point).

I like to add to the above statement that this is only the voltage as imposed on the diaphragm by the electric field (the signal on the plates). The second component that causes the diaphragm voltage to vary is the charge on the diaphragm and the change in capacitance (w.r.t. the plates) with position.
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Old 19th August 2008, 04:18 PM   #29
Nevod is offline Nevod  Russian Federation
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Well, then, I guess, the simulation should include air - and, again, not a simplification of waves - but actual stuff made of molecules. Maybe you don't need every molecule, but at least a some way of modelling them.
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Old 20th August 2008, 02:12 AM   #30
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Nevod,
In acoustic modelling the only parameters that are needed are bulk macroscopic variables (averages of microscopic fluctuations). Mass density fluctuations, volume, sound speed in air, and temperature. In linear acoustics we treat all physical parameters as small perturbations of the static undisturbed medium. If we were considering vibrations of crystal lattices then your right we would treat the atoms making up the solid as an array of coupled harmonic oscillators that are excited by phonons.
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