Open baffles and directivity

Yuihb · 2004-02-22 7:32 pm

To model an open baffel that is not circular, I integrated the function

g:= (f,d,a) -> abs(1+exp(I*phi(f,d,a))); (phi is the pase shift)

that gives the gain for the two-point-source model at frequency f, distance d and angle a to average from 0.4 m to 1 m:

b:= (f,a) -> evalf( Int(g(f,d,a), d=0.4..1)/0.6);

This should correspond to a baffle that is shaped like obfp1.gif:

This is the frequency response on-axis from 50 to 3000 Hz:

There are a lot of peaks and holes due to interference which must be equalized. Still, this response is smoother than that of a circular baffle which has interference holes at all multiples of c/d.

Up to 230 Hz, the radiation pattern is a figure-of-eight. This shape however becomes increasingly distorted at higher freqencies. The following graphs show the radiation pattern at 400, 800, and 1600 Hz:

At 400 Hz, there's a response of almost 2 dB at +/- 45 degrees. At 1600 Hz at lot of energy is radiated almost orthogonal to the main axis which will cause standing waves at least between floor and ceiling while other room modes are likely to be excited as well because of the lack of directivity.

My conclusion is that this baffle is useful in a range from 50 to 230 Hz only. Since it doesn't make sense to construct a different baffle for each interval, I question that open baffles are better than conventional designs. It seems that there are as many advantages as disadvantages.

Boris (yuihb01 at compuserve dot de)

Svante · 2004-02-22 8:54 pm

Yuihb said:
To model an open baffel that is not circular, I integrated the function

g:= (f,d,a) -> abs(1+exp(I*phi(f,d,a))); (phi is the pase shift)

that gives the gain for the two-point-source model at frequency f, distance d and angle a to average from 0.4 m to 1 m:

b:= (f,a) -> evalf( Int(g(f,d,a), d=0.4..1)/0.6);

This should correspond to a baffle that is shaped like obfp1.gif:

This is the frequency response on-axis from 50 to 3000 Hz:

There are a lot of peaks and holes due to interference which must be equalized. Still, this response is smoother than that of a circular baffle which has interference holes at all multiples of c/d.

Up to 230 Hz, the radiation pattern is a figure-of-eight. This shape however becomes increasingly distorted at higher freqencies. The following graphs show the radiation pattern at 400, 800, and 1600 Hz:

At 400 Hz, there's a response of almost 2 dB at +/- 45 degrees. At 1600 Hz at lot of energy is radiated almost orthogonal to the main axis which will cause standing waves at least between floor and ceiling while other room modes are likely to be excited as well because of the lack of directivity.

My conclusion is that this baffle is useful in a range from 50 to 230 Hz only. Since it doesn't make sense to construct a different baffle for each interval, I question that open baffles are better than conventional designs. It seems that there are as many advantages as disadvantages.

Boris (yuihb01 at compuserve dot de)

This is interesting, but I cannot see the images, so I'm having a hard time understanding your math. Could you post the images again?

Yuihb · 2004-02-23 4:23 pm

I'm sorry, something went wrong with the file upload. This is the shape of the baffle:

Yuihb · 2004-02-23 4:24 pm

This is the frequency response:

Yuihb · 2004-02-23 4:25 pm

This is the radiation pattern at 400 Hz:

Yuihb · 2004-02-23 4:26 pm

This is the radiation pattern at 800 Hz:

Yuihb · 2004-02-23 4:28 pm

This is the radiation pattern at 1600 Hz:

Bas Horneman · 2004-02-23 5:27 pm

"Every advantage has it's disadvantages" - Johan Cruiff

Svante · 2004-02-23 5:44 pm

Yuihb said:
To model an open baffel that is not circular, I integrated the function

g:= (f,d,a) -> abs(1+exp(I*phi(f,d,a))); (phi is the pase shift)

that gives the gain for the two-point-source model at frequency f, distance d and angle a to average from 0.4 m to 1 m:

b:= (f,a) -> evalf( Int(g(f,d,a), d=0.4..1)/0.6);

This should correspond to a baffle that is shaped like obfp1.gif:

This is the frequency response on-axis from 50 to 3000 Hz:

There are a lot of peaks and holes due to interference which must be equalized. Still, this response is smoother than that of a circular baffle which has interference holes at all multiples of c/d.

Up to 230 Hz, the radiation pattern is a figure-of-eight. This shape however becomes increasingly distorted at higher freqencies. The following graphs show the radiation pattern at 400, 800, and 1600 Hz:

At 400 Hz, there's a response of almost 2 dB at +/- 45 degrees. At 1600 Hz at lot of energy is radiated almost orthogonal to the main axis which will cause standing waves at least between floor and ceiling while other room modes are likely to be excited as well because of the lack of directivity.

My conclusion is that this baffle is useful in a range from 50 to 230 Hz only. Since it doesn't make sense to construct a different baffle for each interval, I question that open baffles are better than conventional designs. It seems that there are as many advantages as disadvantages.

Boris (yuihb01 at compuserve dot de)

OK, before we go to the conclusions of this (which I sense that I will to some extent agree with you) I would like to get the model straight. From
g:= (f,d,a) -> abs(1+exp(I*phi(f,d,a))); (phi is the pase shift)
it seems as if you add two sources of equal magnitude. I would add four sources, but the result would be the same; on the front side we would see the point source and its mirror, and an edge reflection from the front source and also an edge reflection from the back source. Maybe you "think" four sources as well?
The back edge reflection will have the same sign as the front edge reflection, but the opposite to that of the front source and its mirror. There is a "+" in your equation above,but maybe you fix this in the phi equation?
So, how do you calculate the phase? I suppose you would calculate the pathway for each angle, first from the source to the edge, and then add the distance difference between the edge and the source, seen from the listener? Then integrate over all angles in the baffle plane to sum up all edge sources?
Do you use any directivity of the edge source? I have found this directivity kind of hard to understand from the articles I have read.

My second question is where you got the baffle shape from? Does it represent a rectangular edge distance distribution between 0.4 and 1 m or have you used some other trick? The fluctuations you see in the frequency response will vary *a lot* with the placement on the baffle, and it is likely that you could find a better baffle shape and/or placement.

A third question would be what you mean with "useful"? If you define the usefulness by that the directivity of the speaker should be a dipole, the you are right. It stops being a proper dipole at about 200Hz (for these dimensions). On the other hand I have understood that people like the dipole because it does not excite the room resonances as much as a point source. Room resonances mainly occur at low frequencies (<200Hz). Above this frequency, the baffled speaker will behave in about the same way as a boxed speaker.

I have posted this link here before, but I'll do it again in case you have not seen it. It is a little diffraction hack of mine, that allows you to experiment with different baffle shapes. It uses the model I described above, with the exception that the response is only plotted straight in front of the baffle.
http://www.tolvan.com/diffract.exe

I don't know if I answered your question, or if there was one, but anyway...

Opinions?

Baffle diffraction is fun!

eStatic · 2004-02-24 12:33 am

Re: Re: Open baffles and directivity

Svante said:
On the other hand I have understood that people like the dipole because it does not excite the room resonances as much as a point source. Room resonances mainly occur at low frequencies (<200Hz). Above this frequency, the baffled speaker will behave in about the same way as a boxed speaker.

My shriveled little gray cells seem to recall at least one person here who suggested that another major advantage of dipoles is the production of pseudo ambience. That would be in the range > 200Hz Yes, no?

Bill Fitzpatrick · 2004-02-24 12:58 am

svante:

Nice little program.

If you ever get into the mood to modify it consider the ability to drag the speaker around on the baffle.

Let me know when the new version is ready to download.

ThorstenL · 2004-02-24 1:04 am

Konnichiwa,

Yuihb said:
This is the frequency response on-axis from 50 to 3000 Hz:

There are a lot of peaks and holes due to interference which must be equalized.

Hmmm. If we assume that a flat on axis frequency response is desirable as a thing in itself - yes. But that is a preconception that is not neccesarily supportable.

Yuihb said:
Up to 230 Hz, the radiation pattern is a figure-of-eight. This shape however becomes increasingly distorted at higher freqencies.

Assuming of course a driver that has a perfectly omnidirectional directivity into each direction, with the baffle forming it into 2 X halvespace with opposite polarity, which in reality (rather than science fiction) of course does not happen.

Yuihb said:
The following graphs show the radiation pattern at 400, 800, and 1600 Hz:

Only if a driver "infinitly small" is utilised. It is quite interesting to compare a real driver with 8 - 10" Diameter under identical condition.

Yuihb said:
My conclusion is that this baffle is useful in a range from 50 to 230 Hz only.

Your conclusion with regards to the upper useable limit is based on incomplete considerations and bad models (as in unrealistic models). Using something closer to reality gives a different picture.

Sayonara

Sheldon · 2004-02-24 1:20 am

Re: Re: Open baffles and directivity

Kuei Yang Wang said:
Konnichiwa,

Your conclusion with regards to the upper useable limit is based on incomplete considerations and bad models (as in unrealistic models). Using something closer to reality gives a different picture.

Sayonara

What you assert makes sense, given the non-ideal nature of actual systems, but "bad models" seems a bit harsh (though you did soften it). Virtually all useful mathematical models of messy (realistic) systems begin this way. Gotta start somewhere. It's nice to see the effort given.

Sheldon

ThorstenL · 2004-02-24 8:47 am

Re: Re: Re: Open baffles and directivity

Konnichiwa,

Sheldon said:
but "bad models" seems a bit harsh (though you did soften it). Virtually all useful mathematical models of messy (realistic) systems begin this way.

Hmmm. Perhaps I should have said "Insufciently detailed models to draw useful conclusions", but that sounds stilted, longwinded and boring. I feel "bad model" is more to the point.

I have been repeatedly commenting that modeling speaker performance in pieces (and modeling/measuring them under anechonic conditions) is of little significance, as it failes to predict anything usefull about the actual performace in the real world. I prefer a model that is not exceptionally accurate but attempts to include at least all first order variable much more useful than one that attemps to be execissively accurate but omits virtually all first order variables....

Here some measurements taken on the (front) directivity of Dipoles.....

http://www.gmi.edu/~drussell/GMI-Acoustics/Directivity2.html

Figure2: Student measurements of radiation directivity patterns for a 3-inch loudspeaker with and without a baffle