When tinkering around with this project, I stumbled across something that was very useful. My sims appear to indicate that you can get directivity control to a much lower frequency than you would expect from a device this small. The key is that the two woofers on the edge of the waveguide create an interference pattern, reducing output off axis. The net effect is directivity of a larger device.
Or at least, that's the idea.
I believe @speakerdave did something similar in his Snell eXpanding Arrays, and @bwaslo did it in his 2nd and 3rd Synergy Horn projects. I just didn't really 'grok' what was going on.
Here's the response of a couple of woofers spaced at a distance of 1/3 wavelength. The effect is quite subtle, but it's there. At 45 degrees off axis the output of the array is reduced by 3dB. At 90 degrees off axis, output is down by 6dB. The equivalent of reducing the power by 75%. Not too shabby.
Here's the response of the same array, but I've increased the frequency to 700Hz. Basically a spacing on one-half-wavelength. At this spacing, the beam is much narrower. The danger here is that the pattern will get ugly as you go higher in frequency.
Or at least, that's the idea.
I believe @speakerdave did something similar in his Snell eXpanding Arrays, and @bwaslo did it in his 2nd and 3rd Synergy Horn projects. I just didn't really 'grok' what was going on.
Here's the response of a couple of woofers spaced at a distance of 1/3 wavelength. The effect is quite subtle, but it's there. At 45 degrees off axis the output of the array is reduced by 3dB. At 90 degrees off axis, output is down by 6dB. The equivalent of reducing the power by 75%. Not too shabby.
Here's the response of the same array, but I've increased the frequency to 700Hz. Basically a spacing on one-half-wavelength. At this spacing, the beam is much narrower. The danger here is that the pattern will get ugly as you go higher in frequency.
Trying to figure out where to put the woofers gets a little tricky. In Bill Waslo's "Smally Syns" project the waveguide controls directivity down to about 900Hz.
With a spacing of 10", those two woofers should create an interference pattern that narrows the directivity at approximately 1/3WL, or 450Hz.
Here's the polar response that Bill measured. The woofer array seems to be working nicely. (Copied from here : http://www.diyaudio.com/forums/multi-way/292379-syns.html#post4736721)
This post is going to be super-confusing, please bear with me:
When putting a woofer array adjacent to a waveguide, the interference pattern is different than if the woofers were on a flat baffle. Here's why:
On a flat baffle, the interference pattern is created by a phase difference between the top woofer and the bottom woofer. For instance, the sound of the top woofer is 120 degrees out of phase with the BOTTOM woofer when the sound radiates downwards. (The 120 degree differencie in phase is due to the 1/3WL spacing. One third of a wavelength is 120 degrees.)
On a baffle with a waveguide, the interference pattern is created by a phase difference between the top woofer and the bottom woofer. But the interference is far more complex, because a fraction of the sound is radiated OUT, and a fraction of the radiation goes right down the waveguide's throat.
Take a look at this sim, with the exact same frequency and spacing. The only difference is that the baffle is flat. Note that the FLAT baffle yields a *narrower* directivity. This might not be obvious, you'd think the flat baffle would have wider directivity. The key is the complex relationship between the phase and SPL of the top woofer and the bottom woofer, and the effect of the sound radiating *backwards* when there's a waveguide in the mix.
This is one of those super complex topics that begs for a simulator like Abec. Hornresp will get us 'in the ballpark.' To me, the Hornresp sims appear to indicate that you can move the woofers further apart than one third of a wavelength.
IE, if you have two woofers on a flat baffle, and you're using an interference pattern to control directivity, the maximum spacing is about 1/3rd of a WL. If you have two woofers on a baffle with a waveguide in between them and you're using an interference pattern to control directivity, the sims appear to indicate that you can get away with a spacing between 1/3rd and 1/2 of a wavelength.
Is this a big deal? No, not a huge deal. But I'd argue that you could probably juggle the wall angle of the waveguide and the spacing of the woofers to come up with a nice compromise.
IE, you make be able to use a shallow waveguide, around 120 degrees, and juggle the spacing and the phase of the woofers to get a narrower beam, perhaps 90 degrees.
This could be particularly useful with the smaller Synergy horns, because the output of the woofers could be injected at the mouth, where the waveguide angle is broadening by design.
When putting a woofer array adjacent to a waveguide, the interference pattern is different than if the woofers were on a flat baffle. Here's why:
On a flat baffle, the interference pattern is created by a phase difference between the top woofer and the bottom woofer. For instance, the sound of the top woofer is 120 degrees out of phase with the BOTTOM woofer when the sound radiates downwards. (The 120 degree differencie in phase is due to the 1/3WL spacing. One third of a wavelength is 120 degrees.)
On a baffle with a waveguide, the interference pattern is created by a phase difference between the top woofer and the bottom woofer. But the interference is far more complex, because a fraction of the sound is radiated OUT, and a fraction of the radiation goes right down the waveguide's throat.
Take a look at this sim, with the exact same frequency and spacing. The only difference is that the baffle is flat. Note that the FLAT baffle yields a *narrower* directivity. This might not be obvious, you'd think the flat baffle would have wider directivity. The key is the complex relationship between the phase and SPL of the top woofer and the bottom woofer, and the effect of the sound radiating *backwards* when there's a waveguide in the mix.
This is one of those super complex topics that begs for a simulator like Abec. Hornresp will get us 'in the ballpark.' To me, the Hornresp sims appear to indicate that you can move the woofers further apart than one third of a wavelength.
IE, if you have two woofers on a flat baffle, and you're using an interference pattern to control directivity, the maximum spacing is about 1/3rd of a WL. If you have two woofers on a baffle with a waveguide in between them and you're using an interference pattern to control directivity, the sims appear to indicate that you can get away with a spacing between 1/3rd and 1/2 of a wavelength.
Is this a big deal? No, not a huge deal. But I'd argue that you could probably juggle the wall angle of the waveguide and the spacing of the woofers to come up with a nice compromise.
IE, you make be able to use a shallow waveguide, around 120 degrees, and juggle the spacing and the phase of the woofers to get a narrower beam, perhaps 90 degrees.
This could be particularly useful with the smaller Synergy horns, because the output of the woofers could be injected at the mouth, where the waveguide angle is broadening by design.
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While pondering the interaction of the waveguide and the woofer array, it occurred to me that one solution might be to put the woofers on the BOTTOM of the enclosure, instead of underneath the waveguide. As show in the sims, sound radiating *into* the waveguide is having an impact on the polar response of the woofer array. Moving the woofers to the BOTTOM of the box may reduce that substantially.
Another cool part is that you could make the array symmetrical by putting woofers on the top AND the bottom of the box.
Interesting stuff Patrick.
On your earlier comment:
With DATS I've observed that Fs and Qts usually comes out higher vs factory specs. So the variation that you've got on woofer specs - all of it might not be due to "ageing". 🙂
On your earlier comment:
With DATS I've observed that Fs and Qts usually comes out higher vs factory specs. So the variation that you've got on woofer specs - all of it might not be due to "ageing". 🙂
True. I get the impression that manufactures measure a bunch of drivers and pick the one with the lowest FS and the lowest QTS.
When I measure drivers, they *always* have higher FS and QTS.
When I do sims, I'll sometimes average the published specs and my own measurements. My thought here is that the FS tends to get lower as you use the woofer, sometimes dropping as much as 10%.
Obviously, the ideal would be to break in the woofer for a couple days, but who has time for that?
Don Keele knows way more about arrays and waveguides than I do. He wrote this interesting paper, which forum member Folgott used in a few of his recent projects:
http://www.xlrtechs.com/dbkeele.com...ear Phase Digital Crossover Flters Part 2.pdf
Don is getting constant directivity in his arrays using a spacing of 0.75Wl. This is more than double the spacing that Danley and Waslo are using. I'm no expert on this, but I'd speculate that the secret sauce is the use of FIR filters to manipulate the phase on both sides of the xover point.
In this illustration for the Keele Horbach paper, you can see that the polar pattern gets ugly as the spacing gets larger. So fixing that will require manipulation of the phase of the array, I think.
http://www.xlrtechs.com/dbkeele.com...ear Phase Digital Crossover Flters Part 2.pdf
Don is getting constant directivity in his arrays using a spacing of 0.75Wl. This is more than double the spacing that Danley and Waslo are using. I'm no expert on this, but I'd speculate that the secret sauce is the use of FIR filters to manipulate the phase on both sides of the xover point.
In this illustration for the Keele Horbach paper, you can see that the polar pattern gets ugly as the spacing gets larger. So fixing that will require manipulation of the phase of the array, I think.
While pondering what I said in post 63 (Soundbar Bateman Style) I realized something:
The sims seem to indicate that woofers adjacent to a waveguide can be spaced further apart that woofers on a flat baffle.
I need to do some more sims, but I'm starting to think this isn't the case. Here's why:
The reason that the sims looks so good when the drivers are seperated by one half wavelength is because the sound is 100% out-of-phase when you're off-axis by 90 degrees. This is because of the pathlength difference. When you have two woofers on a flat baffle and they're spaced one half wavelength apart, then the two drivers will be 100% out of phase when you're 90 degrees off axis.
This is fairly basic; the pathlength difference creates a null off axis.
With a waveguide in the mix, things get more complex.
But the improvement in the polars when the waveguide is in the mix doesn't change the laws of physics. What's happening is that the pathlength *down* the waveguide is longer. (Because sound has to go down the waveguide, reflect off the throat, and come back out.)
So it doesn't mean that the addition of a waveguide allows a broader spacing. In fact, it might require a tighter spacing. (Again, because the sound has to go down the waveguide and back out.)
All of this is hideously complex. I would speculate that if you're using conventional filters or passive filters, you probably don't want the drivers spaced more than one third of a wavelength.
If you know what you're doing, and you can implement FIR filters, you can do some interesting things to control the directivity of the loudspeaker by manipulating the phase to change the polar response.
The sims seem to indicate that woofers adjacent to a waveguide can be spaced further apart that woofers on a flat baffle.
I need to do some more sims, but I'm starting to think this isn't the case. Here's why:
The reason that the sims looks so good when the drivers are seperated by one half wavelength is because the sound is 100% out-of-phase when you're off-axis by 90 degrees. This is because of the pathlength difference. When you have two woofers on a flat baffle and they're spaced one half wavelength apart, then the two drivers will be 100% out of phase when you're 90 degrees off axis.
This is fairly basic; the pathlength difference creates a null off axis.
With a waveguide in the mix, things get more complex.
But the improvement in the polars when the waveguide is in the mix doesn't change the laws of physics. What's happening is that the pathlength *down* the waveguide is longer. (Because sound has to go down the waveguide, reflect off the throat, and come back out.)
So it doesn't mean that the addition of a waveguide allows a broader spacing. In fact, it might require a tighter spacing. (Again, because the sound has to go down the waveguide and back out.)
All of this is hideously complex. I would speculate that if you're using conventional filters or passive filters, you probably don't want the drivers spaced more than one third of a wavelength.
If you know what you're doing, and you can implement FIR filters, you can do some interesting things to control the directivity of the loudspeaker by manipulating the phase to change the polar response.
My apologies for all the rambling tonight, when I'm trying to figure out a patent or a paper I like to put my thoughts on the forum. Helps me figure things out.
After studying the Horbach Keele paper for a few hours, I believe I figured out why the elements are spaced the way they are.
And I believe Horbach Keele filters could be used to create something like Bill's "Small Syns" horn. The catch is that the spacing will need to be much wider than the picture above.
OK, here's how the Horbach Keele filters work, as I understand it:
In the Horbach Keele array, the drivers are spaced at about 0.75 wavelengths. This is a bit unusual, because most MTM arrays use a spacing that's very tight (like the Snell Expanding array) or very loose (like the D'Appolito array.)
But the Horbach Keele spacing is about 0.75WL.
What's happening is that there's something called "the critical frequency" where only TWO drivers in the entire array are playing. You could have an array of three element or 99 elements, at the critical frequency only two drivers are playing.
The "critical frequency" is quite a bit higher than the xover point. It corresponds to approximately one half wavelength. For instance, the 4" midranges in the Horbach Keele speaker are nine inches apart. 1500Hz is nine inches long. One half of that is 750Hz. The 'critical frequency' of the 4" midranges in the Horbach Keele speaker is 825Hz. IE, it's approximately one half wavelength of the distance between the two drivers.
My 'Eureka Moment' was when I realized that the Horbach Keele speaker is an array of arrays at the xover point. For instance, in a traditional D'Appolito speaker, there is a two element array of woofers. But the Horbach Keele speaker is different. At the xover frequency, you have four drivers playing. So the top two drivers form an array of two drivers, the bottom two drivers form an array of two drivers, and there's an an array of those two pairs.
An array of arrays.
So that's why the spacing is at 0.75WL. At the xover point, there are four drivers playing, and due to that, there are two acoustic sources. (One at the top, one at the bottom.) And those acoustic sources radiate from a point between the two elements.
Very cool!
That's how the Horbach Keele speaker gets such smooth polar response. As the frequency gets lower and lower, you have two sources that radiate from a distance that increases.
You could take this to crazy extremes; if you had a very tall ceiling you could maintain directivity control down to 20Hz. This would also be very cool for a concert or the like.
Obviously, it's incredibly wasteful in terms of DSP and amplifier power! Each driver is playing over a very narrow bandwidth.
Of course, this is a thread about a Synergy Horn Boombox. In that context, the advantage of the Keele Horbach filters is the ability to control directivity in a relatively compact package. For instance, a 90 degree waveguide that controls directivity down to 500Hz measures 27" wide by 13.5" deep. That's why the Danley SH-50 looks like this:
But with Horbach Keele filters, you can directivity control down to 500Hz with an array that's less than 25% of the size. This is because the width and height can be about half the size, and the depth can be extraordinarily shallow.
You can also make the array symmetrical, or combine it with a different array type for the other axis. Here is Ulrich Horbach with his latest creation.
After studying the Horbach Keele paper for a few hours, I believe I figured out why the elements are spaced the way they are.
And I believe Horbach Keele filters could be used to create something like Bill's "Small Syns" horn. The catch is that the spacing will need to be much wider than the picture above.
OK, here's how the Horbach Keele filters work, as I understand it:
In the Horbach Keele array, the drivers are spaced at about 0.75 wavelengths. This is a bit unusual, because most MTM arrays use a spacing that's very tight (like the Snell Expanding array) or very loose (like the D'Appolito array.)
But the Horbach Keele spacing is about 0.75WL.
What's happening is that there's something called "the critical frequency" where only TWO drivers in the entire array are playing. You could have an array of three element or 99 elements, at the critical frequency only two drivers are playing.
The "critical frequency" is quite a bit higher than the xover point. It corresponds to approximately one half wavelength. For instance, the 4" midranges in the Horbach Keele speaker are nine inches apart. 1500Hz is nine inches long. One half of that is 750Hz. The 'critical frequency' of the 4" midranges in the Horbach Keele speaker is 825Hz. IE, it's approximately one half wavelength of the distance between the two drivers.
My 'Eureka Moment' was when I realized that the Horbach Keele speaker is an array of arrays at the xover point. For instance, in a traditional D'Appolito speaker, there is a two element array of woofers. But the Horbach Keele speaker is different. At the xover frequency, you have four drivers playing. So the top two drivers form an array of two drivers, the bottom two drivers form an array of two drivers, and there's an an array of those two pairs.
An array of arrays.
So that's why the spacing is at 0.75WL. At the xover point, there are four drivers playing, and due to that, there are two acoustic sources. (One at the top, one at the bottom.) And those acoustic sources radiate from a point between the two elements.
Very cool!
That's how the Horbach Keele speaker gets such smooth polar response. As the frequency gets lower and lower, you have two sources that radiate from a distance that increases.
You could take this to crazy extremes; if you had a very tall ceiling you could maintain directivity control down to 20Hz. This would also be very cool for a concert or the like.
Obviously, it's incredibly wasteful in terms of DSP and amplifier power! Each driver is playing over a very narrow bandwidth.
Of course, this is a thread about a Synergy Horn Boombox. In that context, the advantage of the Keele Horbach filters is the ability to control directivity in a relatively compact package. For instance, a 90 degree waveguide that controls directivity down to 500Hz measures 27" wide by 13.5" deep. That's why the Danley SH-50 looks like this:
But with Horbach Keele filters, you can directivity control down to 500Hz with an array that's less than 25% of the size. This is because the width and height can be about half the size, and the depth can be extraordinarily shallow.
You can also make the array symmetrical, or combine it with a different array type for the other axis. Here is Ulrich Horbach with his latest creation.
Hi John
Now that people have finally figured out how important directivity is, there are a few features that come in very handy.
1) the directivity of a combination of sources can be found as the product of different sources that combined create the desired source. For example two 3" disks spaced apart is the product of the directivity of a single 3" disk and a doublet of the same spacing.
2) directivity is linear so combinations of sources add linearly. For example the polar response of an annular disk is the directivity of the outer solid disk minus the directivity inner disk.
Thinking this through, one can see that if you were to plot some desired directivity function (pressure versus angle) you could achieve this by simply expanding the desired function into a sum of known functions or products of functions. In this way any directivity could be achieved.
As to the Keele approach, I have argued this point with Don many times. He wants to control the vertical response, but leaves the horizontal response as is (usually bad). My goal is dominantly to control the horizontal response to limit a devices interaction with the walls in a small room. Vertical control is the domain of large venues, not small ones.
Now that people have finally figured out how important directivity is, there are a few features that come in very handy.
1) the directivity of a combination of sources can be found as the product of different sources that combined create the desired source. For example two 3" disks spaced apart is the product of the directivity of a single 3" disk and a doublet of the same spacing.
2) directivity is linear so combinations of sources add linearly. For example the polar response of an annular disk is the directivity of the outer solid disk minus the directivity inner disk.
Thinking this through, one can see that if you were to plot some desired directivity function (pressure versus angle) you could achieve this by simply expanding the desired function into a sum of known functions or products of functions. In this way any directivity could be achieved.
As to the Keele approach, I have argued this point with Don many times. He wants to control the vertical response, but leaves the horizontal response as is (usually bad). My goal is dominantly to control the horizontal response to limit a devices interaction with the walls in a small room. Vertical control is the domain of large venues, not small ones.
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Lexicon SL-1 SoundSteer | Hi-Fi | News | AVHub
Note Lexicon isn't using wave guides to do much of this. Drivers don't look particularly special either. Symmetrical design likely allows for most flexibility. I suspect the cabinet shape works with the back waves as well as giving the full surround shape.
Ulrich is with Harmon. Dirac involved with Harman and Lexicon.
The original post mentioned trying to set center channel separation up using speaker shape instead of physical barrier. DSP is another option. It looks like they are going for a 1.1 system to do it all !!!
Grant.
Doing one is difficult enough. Trying to do both adds more complexity and usually results in lessor performance than doing one alone.
But it depends on what directivity you are looking for. My speakers have controlled directivity in both directions, but its the same. What one usually wants is narrower in the vertical and that gets tough resulting in a degradation of the horizontal. I consider the horizontal paramount in a small room and control the vertical with room treatment.
I am going to study this post and try to make sense of it. I don't understand how to compute the product of directivity of a disk, so additional study will be required.
As noted in another post, there's no software that can compute the polar response of an array that includes crossovers. (Ridiculous, isn't it?)
ABEC can do it, but I don't have two years to put together a mesh.
The best that I can do with limited (software) resources is model the behavior of the array using a low and a high pass.
IE, ideally I'd model the entire loudspeaker, and their crossover filters. But the software that I have can only do high pass or low pass. It can't do bandpass.
Here's the response of the dual 2" midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the midrange array with a highpass filter. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequency is 2475Hz, and you can see that the directivity narrows in this sim.)
Here's the response of the dual 4" lower midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the lower midrange array with a lowpass filter. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequency is 825Hz, and you can see that the directivity narrows in this sim.)
Here's the response of the dual 4" lower midranges AND the dual 2" uppper midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the lower midrange and upper midrange array with a lowpass and a highpass filter, respecitvely. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequencies are 825Hz and 2475Hz, and you can see that the directivity narrows in this sim.)
The primary takeaway here is that the array of four drivers has narrow directivity over a bandwidth of about two octaves from 750Hz to 3000Hz. This is achieved without the use of waveguides, in a package that's remarkably small.
Here's a speaker using the topology, with the inventor of the filter. Note how compact the loudspeaker is.
These sims are probably a bit confusing. The general idea is that the spacing of the array elements, the crossover filter and the crossover point creates an interference pattern that narrows the directivity of the array over a narrow bandwidth.
The bandwidth is important here; each pair of elements only works over about one octave. The directivity illustrated in the final sim isn't as good as the Horbach Keele paper. This is because the Horbach Keele paper uses a very specific filter shape designed to achieve constant directivity.
In the sim posted above, I'm using 4th Order LR4 filters. They're not as 'perfect' as the Horbach Keele filter, but they're close. The main part of the 'secret sauce' is the spacing of the midranges and the crossover points.
ABEC can do it, but I don't have two years to put together a mesh.
The best that I can do with limited (software) resources is model the behavior of the array using a low and a high pass.
IE, ideally I'd model the entire loudspeaker, and their crossover filters. But the software that I have can only do high pass or low pass. It can't do bandpass.
Here's the response of the dual 2" midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the midrange array with a highpass filter. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequency is 2475Hz, and you can see that the directivity narrows in this sim.)
Here's the response of the dual 4" lower midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the lower midrange array with a lowpass filter. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequency is 825Hz, and you can see that the directivity narrows in this sim.)
Here's the response of the dual 4" lower midranges AND the dual 2" uppper midranges from the Horbach Keele paper. In this sim, I've set the diameter of the mids, the spacing and the xover point to the same frequency that's in the paper. I can't model a bandpass filter, so here's the response of the lower midrange and upper midrange array with a lowpass and a highpass filter, respecitvely. At the 'critical frequency', the spacing of the elements is narrowing the directivity of the array, as the Horbach Keele paper predicts. (The critical frequencies are 825Hz and 2475Hz, and you can see that the directivity narrows in this sim.)
The primary takeaway here is that the array of four drivers has narrow directivity over a bandwidth of about two octaves from 750Hz to 3000Hz. This is achieved without the use of waveguides, in a package that's remarkably small.
An externally hosted image should be here but it was not working when we last tested it.
Here's a speaker using the topology, with the inventor of the filter. Note how compact the loudspeaker is.
These sims are probably a bit confusing. The general idea is that the spacing of the array elements, the crossover filter and the crossover point creates an interference pattern that narrows the directivity of the array over a narrow bandwidth.
The bandwidth is important here; each pair of elements only works over about one octave. The directivity illustrated in the final sim isn't as good as the Horbach Keele paper. This is because the Horbach Keele paper uses a very specific filter shape designed to achieve constant directivity.
In the sim posted above, I'm using 4th Order LR4 filters. They're not as 'perfect' as the Horbach Keele filter, but they're close. The main part of the 'secret sauce' is the spacing of the midranges and the crossover points.
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It would be interesting to hear this speaker set up with no DSP at all and again with the midrange spacing changed. That would tell a lot.
Grant.
My now obsolete SPEAK software could do that well over 20 years ago.
To explain my point a little better consider:
Two pistons of radius a separated apart by x and radiating at wavenumber k.
This is equivalent to a single piston imposed on two point sources separated by x. The piston directivity is J0( k*a*sin(theta))/(k*a*sin(theta)) (where J0 is the Bessel function of order 0) and the two point sources are cos(k*x*sin(theta)). Hence the total pattern is:
J0( k*a*sin(theta)) * cos(k*x*sin(theta)) / (k*a*sin(theta))
With this result one can work backwards from the desired response to the required a and x. With sims you can't do that, only calculate what you will get for a given a and x.
Do you believe the floor reflection adds anything to the naturalness of a speaker system? Do you think you could reduce it to imperceptible levels without negatively impacting the listening experience?
First consider that our ears are in the horizontal plane, which means that we are inherently far more sensitive to sound in that plane than the vertical one. That said vertical reflections are never a good thing, but the extent to which they are objectionable is debatable. Griesinger says that we simply ignore vertical reflections, others have shown that they are certainly audible.
So no, floor (or ceiling) reflections do not add anything. Can they be reduced ti "imperceptible", sounds tough! But I do diffuse the ceiling and absorb the floor with a very thick rug, but I can still measure a reflection, although it is quite muted. The negative impacts appears to be minimal if not imperceptible.
But the horizontal directivity control is paramount as this dictates imaging and spaciousness, the very essence of musical listening.
So no, floor (or ceiling) reflections do not add anything. Can they be reduced ti "imperceptible", sounds tough! But I do diffuse the ceiling and absorb the floor with a very thick rug, but I can still measure a reflection, although it is quite muted. The negative impacts appears to be minimal if not imperceptible.
But the horizontal directivity control is paramount as this dictates imaging and spaciousness, the very essence of musical listening.
I visited your site Earl and it looks like SPEAK is available for a free download for people that are interested. It looks like there's enough there to keep someone busy for a couple minutes ;-).
Thanks.
Grant.
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