Geddes on Waveguides

One more time and maybe I can make this a littlke clearer so that everyone can follow it.

Power(f) = R * V(f)^2, where R is the radiation impedance (real part) and V(f) is the frequency dependent source velocity. This is a fundamental law of physics and is not open to argument.

Now Power(f) is also the integral of Pres(f) ^2 over a surface enclosing the source (think of just summing all the points on a sphere), where Pres(f) is the pressure response, another fundamental relationship in physics that is beyond question.

Now back to the first equation. R is the radiation impedance and it is also well know that this term always becomes flat - independent of frequency - at higher frequencies, -this is true of any source with a waveguide, horn or not. Lets assume that we have CD, then Pres(f) is not dependent on directivity and the Power(f) will go as the square of Pres(f). Now if further, Pres(f) is flat (independent of f) on axis (or any axis since it is CD), then it's simple to see that the Power(f) will be independent of f and the pressure is independent of direction. This is what makes CD desirable.

This all means that if the Power(f) is independent of frequency then the velocity of the source must also be independent of frequency. But no source acts like this, all sources are resonant devices and above resonance the velocity must fall at -6 dB/oct (for a constant source voltage). This means that if the device is CD and uses any normal non-EQ'd source that the Power(f) must fall at -12 dB/oct above resonance and at higher frequencies. This equates to a pressure response that falls at -6 dB/oct for any real source which exhibits constant directivity.

A piston source has a changing directivity and it just so happens that its directivity narrows at precisely the same rate that the power falls. This yields a pressure response on axis that is independent of frequency, but the source is, of course, not CD and its power response falls with frequency.

The extent to which any source is CD can be seen quite simply by looking at the HF falloff. If it is less than -6 dB then it must be getting narrower at HF - 0dB (i.e. flat) and its directivity must be narrowing as a piston (narrowest) and if it is -6 dB then its directivity is not changing, i.e. CD. All real sources will lie somewhere between these two extremes.

This is all simple math and if your results do not agree with these then they are incorrect and you should try and figure out what you did wrong.

Eureka! :worship: Thank you.

Man I need a beer.

Dan
 
What you posted before was a polar response and from 100 Hz and up. Were there reflections in that data or not?


LF are always a measurement problem, but I don't believe that they have any meaning in a free field. LF are dominated by the room and the sourcxe is all but irrelavent. Its the HF where gating works fine that I am concerned with and indoor gated measurements work just fine.
 
Doing some investigation on compression effects, it seems the compression driver tends to provide a constant power response? If this is true, shouldn't an OS provide a flat response without EQ?
I thought I throw this sim data up to see what points of views anyone has.
 

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What kind of point of view could anyone have with so little info? Sound power of a lawnmower in the rain?

To answer your quoted question; no, compression drivers do not produce constant power response, they can't. Above what has been called the "mass break point" (where the mass reactance equals the damping), the power response has to fall. IF compression drivers DID produce constant power THEN an OS waveguide would be flat. But that is not the case.
 
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That is basically a sim of around 39mm diameter concaved dome diapragm operating with a 26mm diameter throat coupled with an OS wave guide. Since the polar data looks really nothing like CD should with the high frequencies rising, I did not post them. It was the fact the there was a flat power response that I found interesting. The driver is not a realy driver, just taking the parameters of a 1" driver and changing the diaphragm diameter.
 
Update. From a whole bunch of data from sims, I decided that the configuration for this data (23cm diameter at baffle blending edge) is interesting enough to test. Pretty close to an OS. What really worries me is that manufacturing tolerances seem pretty critical.

George,
Have you, or do you plan to, post a drawing of this contour?
 
Hi Paul,
I am still thinking about it and have to discuss in internally. Lots of work is going into it. Hoping it will end up in a commercial product, but really have not explored the manufacturing options yet, which in many of my work, have become a obstacle to affordable product.
 
..but really have not explored the manufacturing options yet, which in many of my work, have become a obstacle to affordable product.

I've mentioned this before.. Thermoformed, probably with a thin HDPE. Let the customer "back-fill" the waveguide (..which they were going to do anyway unless it was turned wood or an expanded foam).

Material cost is low (less than 10 US per unit), and after a bit of practice with temp control the labor is moron-simple. (..you can also stack it to keep shipping costs low.)
 
I would think that pricing is not really taking into account the mold costs and setup chargers you would incur. I would suspect you would need to make many 100's if not 1000's to get the cost per unit that low.

For example, i contacted a company capable of thermoforming uploaded designs at what they said was the best pricing around. For less than 50 I had an initial 200 dollar setup fee for items in the size I wanted. What I had designed was a record mat made of a plastic material with a dish toward the center, I figured if I could get them cheap enough, it might be something to sell on ebay, and get me a nice record mat that did what I wanted. Cost per unit, on top of that 200 dollars, was 25 dollars per unit. My total cost, after shipping, was around 35 dollars per item. This was for basically a 4mm disc, and the price was still only so low because the form was so simple for them to make.