I will try to use the use a specified DI as the target of the optimization, it seem like an intuitive way to specify the characteristics. However I cant figure out how to calculate the sound power. Looking into the ANSI-CTA-2034-A it says that you should:
1. Convert all responses from SPL to pressure
2. Weigh the individual responses according to the surface area on the sphere they are covering
3. Calculate the RMS value of the weighed responses
4. Convert back to SPL
Is point 3 really correct? Doesn't it make more sense to just take the sum of the weighted responses instead? (at least that creates some realistic results)
Or maybe I did some error converting the weighting factors to halfspace..
1. Convert all responses from SPL to pressure
2. Weigh the individual responses according to the surface area on the sphere they are covering
3. Calculate the RMS value of the weighed responses
4. Convert back to SPL
Is point 3 really correct? Doesn't it make more sense to just take the sum of the weighted responses instead? (at least that creates some realistic results)
Or maybe I did some error converting the weighting factors to halfspace..
To me it's pretty obvious.
As the coverage angle gets wider the DI drops, no surprises there.
As the device gets larger, the point where they all converge goes lower.
Hence, if you want a high DI to a low frequency you will need a large device. A lower DI can be obtained with a smaller device.
This all seems quite predictable to me.
What other equation could one use?
The sims here use what is called the boundary element method (BEM) which takes the 3D Helmholtz equation and through a theorem (forgot its name right now, Kirchhoff-Helmholtz?) one converts the volume field equations into equations on just the boundary surface. Hence only the boundary needs to be specified and the internal pressures calculated from that.
It is, of course, possible to to the calcs using a FEA method, but this is much slower and I doubt that ABEC goes that route - but they could. ANSYS and NASTRAN both use FEA approaches.
What is not obvious to me is why a higher DI doesn't converge flat at all? Are the devices used still too small for that?
To calculate the power you need to find RMS pressure (not dB) squared. Divided by the area you will get intensity (with some constants.) The Sound Power is the integral of this intensity over a sphere.
You cannot convert back to SPL because this is now a Power not a pressure.
This is really not obvious to me - it is not flat even where the wavelengths are much smaller than the mouth size. Isn't it strange?
I don't know, Charlie links to a paper about diffraction models at the end of this post. https://www.diyaudio.com/forums/mul...dence-infinite-baffle-ism-10.html#post6416480 DonVK has been using same sim to model it as here.
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You mean above the convergence point?
There is still going to be some diffraction and HOMs, so perfectly flat is not realistic.
There is still going to be some diffraction and HOMs, so perfectly flat is not realistic.
This is how I do it. C1, C2, ... C37 being the pressures, starting at 0 deg and continue in 5 deg increments up to 180 deg.
Now to calculate DI for the response C1:
C1^2 / (0.000475889*C1^2 + 0.003801680*C2^2 + ... + 0.000475889*C37^2)
You can now make square root of this and convert to SPL (20*log()) or just use 10*log().
Is that correct? I hope so 🙂
Yet it is flat for some coverage angles. Seems like there's always some value of the nominal coverage angle that results in a flat DI curve. Not higher, not lower.
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One cannot specify Sound Power in SPL. It has to be in watts. Sound Power Level (SPL - very bad acronym!!) is in dB, but 10*log(Sound Power)
Yes, I agree with your equation except that I cannot know if the constants are right - they need to be the inverse of the corresponding areas.
It is interesting to know that when one does a modal representation of the field, like I do in my software (same as Klippel) then the sound power is just the sum of the modal coefficients - a trivial calculation. That's how I calculate sound power and DI. Some numerical problems at LFs, but otherwise works well.
Yes, I agree with your equation except that I cannot know if the constants are right - they need to be the inverse of the corresponding areas.
It is interesting to know that when one does a modal representation of the field, like I do in my software (same as Klippel) then the sound power is just the sum of the modal coefficients - a trivial calculation. That's how I calculate sound power and DI. Some numerical problems at LFs, but otherwise works well.
I will give it a try. My only concern with using the DI as an optimization objective is whether you could have a smooth DI but still have diffraction problems. We will see
I see your point. But if they all converge at some LF and they have to end up at different HF DI, then they have to curve. Remember that as the device gets larger the LF DI has to rise, not the other way around. This is going to cause different sizes to interact with the coverage angle and DI in different ways.
It could be that for some given size there is a flattest coverage angle. That would not surprise me at all.
There's a paper by a guy named Nils Öllerer about this very issue (I think it was Dmitrij who postes the link): http://hannover-hardcore.de/infinity_classics/!!!/Buendelungsmass in VACS.pdf
Me neither but it seems to work 🙂
I consider anyone who ever wrote a paper as smarter than me so I just simply used that formula - and as it seemed to work, I haven't studied it further 😱
I consider anyone who ever wrote a paper as smarter than me so I just simply used that formula - and as it seemed to work, I haven't studied it further 😱
I think that you can simply take 10*log() of the result of the formula above and use that as the DI value in dB.
That it is possible to place this curve in the same chart/scale as SPL curves is just a convenience. They are not the same quantity, so my "convert to SPL" was wrong. The numbers are OK, though.
That it is possible to place this curve in the same chart/scale as SPL curves is just a convenience. They are not the same quantity, so my "convert to SPL" was wrong. The numbers are OK, though.
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I don't see how that could happen but maybe my imagination is not big enough.
I too would suspect that its not possible. The DI takes into account almost everything that a source does. I don't see how there could be diffraction and not seen in the power and hence DI.
Along with the frequency response on the DI axis (had to add this to be clear.)
Along with the frequency response on the DI axis (had to add this to be clear.)