How much does it change by frequency?
I know it changes some, just like acoustical centers change some by frequency.
But those changes with frequency have seemed comparatively minor, to the grosser issue of near-field vs far.
I guess this where the 3x rule of thumb comes in....get far enough away to be safe, to get all frequencies out of the near-field.
(Although sometimes lately, my synergy measurements make me question if 3x is really far enough.)
It seems there's some confusion about near- vs far-field.
An explanation (from Principles of sound radiation by Keith R. Holland):
Near- and far-fields
A point monopole source radiates a spherically symmetric sound field in which the acoustic pressure falls as the inverse of the distance from the source (p ∞ 1/r). On the other hand, the particle velocity does not obey this inverse law, but instead falls approximately as 1/r for kr > 1 and 1/r² for kr < 1. The region beyond kr=1, where both the pressure and particle velocity fall as 1/r, is known as the hydrodynamic far-field. In the far-field, the propagation of sound away from the source is little different from that of a plane progressive wave. The region close to the source, where kr < 1 and the particle velocity falls as 1/r2, is known as the hydrodynamic near-field. In this region, the propagation of sound is hampered by the curvature of the wave, and large particle velocities are required to generate small pressures. It is important to note that the extent of the hydrodynamic nearfield is frequency dependent.
The behaviour of the sound field in the hydrodynamic near-field can be explained as follows. An outward movement of the particles of air, due to the action of a source, is accompanied by an increase in area occupied by the particles as the wave expands.
Therefore, as well as the increase in pressure in front of the particles that gives rise to sound propagation, there exists a reduction in pressure due to the particles moving further apart. The ‘propagating pressure’ is in-phase with and proportional to the particle velocity and the ‘stretching pressure’ is in-phase with and proportional to the particle displacement. As velocity is the rate of change of displacement with time, the displacement at high frequencies is less than at low frequencies for the same velocity, so the relative magnitudes of the propagating and stretching pressures are
dependent upon both frequency and radius.
The situation is more complex when finite-sized sources are considered. A second definition of the near-field, which is completely different from the hydrodynamic near-field described above, is the geometric near-field. The geometric near-field is a region close to a finite-sized source in which the sound field is dependent upon the dimensions of the source, and does not, in general, follow the inverse-square law.
The extent of the geometric near field is defined as being the distance from the source within which the pressure does not follow the inverse-square law.
An explanation (from Principles of sound radiation by Keith R. Holland):
Near- and far-fields
A point monopole source radiates a spherically symmetric sound field in which the acoustic pressure falls as the inverse of the distance from the source (p ∞ 1/r). On the other hand, the particle velocity does not obey this inverse law, but instead falls approximately as 1/r for kr > 1 and 1/r² for kr < 1. The region beyond kr=1, where both the pressure and particle velocity fall as 1/r, is known as the hydrodynamic far-field. In the far-field, the propagation of sound away from the source is little different from that of a plane progressive wave. The region close to the source, where kr < 1 and the particle velocity falls as 1/r2, is known as the hydrodynamic near-field. In this region, the propagation of sound is hampered by the curvature of the wave, and large particle velocities are required to generate small pressures. It is important to note that the extent of the hydrodynamic nearfield is frequency dependent.
The behaviour of the sound field in the hydrodynamic near-field can be explained as follows. An outward movement of the particles of air, due to the action of a source, is accompanied by an increase in area occupied by the particles as the wave expands.
Therefore, as well as the increase in pressure in front of the particles that gives rise to sound propagation, there exists a reduction in pressure due to the particles moving further apart. The ‘propagating pressure’ is in-phase with and proportional to the particle velocity and the ‘stretching pressure’ is in-phase with and proportional to the particle displacement. As velocity is the rate of change of displacement with time, the displacement at high frequencies is less than at low frequencies for the same velocity, so the relative magnitudes of the propagating and stretching pressures are
dependent upon both frequency and radius.
The situation is more complex when finite-sized sources are considered. A second definition of the near-field, which is completely different from the hydrodynamic near-field described above, is the geometric near-field. The geometric near-field is a region close to a finite-sized source in which the sound field is dependent upon the dimensions of the source, and does not, in general, follow the inverse-square law.
The extent of the geometric near field is defined as being the distance from the source within which the pressure does not follow the inverse-square law.
I will have to try this...I take you've already tried this with frequencies under a KA=0.5 or tested woofer??? How big of a difference in spl are we talking here?
I agree but if building for a close position like 1 meter you wouldn't want directivity from the mid woofer unless the ka was low enough to keep a 0 transfer function... but back to what you are saying, it still confuses me some...You are talking about running the woofer to a point where Di matches the waveguide at XO I believe. I don't understand how that is possible if the waveguide doesn't match the directivity of the woofer through every other frequency not just the cross band...2 different sources with non identical polars....having matching Di at some frequency...how????
With a woofer and waveguide crossed low enough both sources would be omnidirectional at XO...thus, matching polar...no?
What is the optimum listening distance your current system btw???
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The woofer gains directivity as frequency increases, the waveguide will lose directivity at some point and get wider as frequency goes down.
By matching the directivity of the two at the crossover point it allows the high DI of the waveguide to be maintained to a lower frequency and it is then a smooth downward trend until the woofer loses directivity completely.
There is no need for both devices to match anywhere other than the crossover region. Outside the crossover region both drivers will produce less and less output until they are operating alone.
Running the waveguide until it loses all pattern control to cross low to a woofer with a similar pattern puts a lot of demands on the high frequency driver. With a driver like the Axi this becomes an option with a lot of other drivers it is not feasible or would limit the output too much.
Me too
.The only reason I expressed it the way that I did was to hopefully avoid any confusion - by separating out the 'k' and 'a' components of ka (k * a) so that the formula for wave-number k (2 * Pi * f / c or 2 * Pi / wavelength) was identified specifically.
Leo Beranek uses circumference / wavelength also, in his "Acoustics" book.
I wish I could see an example of this play out...the only way I can visualize this is for one, its planned out, meaning the drivers n waveguide are picked to match each other....but to give you my perspective; I see directivity as attached to dimension...with a waveguide, the dimensions of the opening, the woofer the dimension of its opening and thus, it will be impossible to match polars unless the dimensions are matched...and following...the polar will identical everywhere else as well....I know this is not exactly dead on to the differences between compression driver exit and woofer size? Still I cant be far off either
Don't forget about the baffle width. I am not sure about your seaming confusion matching directivity at crossover is an relatively old concept well 80's and there are lot of systems out there.
Rob
Improvements in Monitor Loudspeaker Systems
Yeah, i've tried it with various 18" and 12" in their own cabinets.
It's not really about SPL differences, or at least that's not how i would characterize it.
It's about comparing the different distance transfer function sets.... how they much each set varies from its on-axis to off-axis, at the same measurement angles.
The near-field set has plenty more variation than the far-field set, no matter what driver I've tried.
Although that said, an 18" doesn't vary comparatively too much for only 150Hz and below....(which is as high as i like to use one).
A 12" however, often needs to reach to 650Hz in my designs, and there Ka is about 1.8.....this does show the increased near-field variance (just like the 18" does at higher freq usage)
Thx for that Ro,
I take it the "geometric near-field" description (which is what i've been going by) is really just a lump-sum default way of saying, "well the speaker doesn't behave as if it's in the far-field and we don't have a great way to say what's really going on, so we'll just call that near-field" hahahaha
Oh, in the first definition ...the point monopole, hydrodynamic one... what's the value of k ?
Don't forget about the baffle width. I am not sure about your seaming confusion matching directivity at crossover is an relatively old concept well 80's and there are lot of systems out there.
Rob
Improvements in Monitor Loudspeaker Systems
Matching polars at xo is not my concern...how one does this with two different sources of different sizes sounds impossible....if the sources are identical in size then the polar matches no matter where you cross it...this is my confusion...if a waveguide vs woofer... both with matching diameter, then where exactly doesnt the polar match? If high enough the directivity will exceed the waveguide...but below that point it would seem options would be open.
My guess is that first we have to start with similar sized waveguide and woofer...second, due to the may be slightly unique directivity of the wave game versus the woofer of the same diameter, there must be only a certain portion of that where the polar actually matches each other… Is this what we are looking for here?
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When crossing a cone driver to a horn the cone will narrow as frequency rises, the horn will widen as frequency goes down. There will be a point where the patterns are the same at least in the horizontal. The smaller the cone driver the higher that point will be. In order to try and keep the directivity constant to a lower frequency the cone driver needs to be larger and the horn it matches with correspondingly larger.
The polars will certainly not match over the entire frequency range.
This is about right
This is from Earl's philosophy document
With the higher frequencies under control, this leaves the mid frequency aspects of the problem to be addressed. First it is essential to match the directivity of the woofer to that of the waveguide. This is a necessary requirement, but one that is often ignored. It is not enough to simply use a CD device in the system, one must insure that the entire system is CD and this means that the LF driver must have the same polar pattern, at the crossover, as the waveguide. A simple investigation will show that only large woofers can provide this feature since a smaller woofer would require the crossover point to be much too high before the polar pattern was at or below 90°. When a piston woofer is used, CD can only go down to just below the crossover point, so the crossover point needs to be as low as practicable. A 15" driver is the smallest device that can be used if a crossover point below 1 kHz is to be achieved. The woofer in the Summa system is 6 dB down at 45° at 800 Hz. Below this frequency their directivity begins to widen. Matching a 15" woofer to a waveguide at 800 Hz is a workable solution. A narrower directivity than 90°, or a lower crossover point would require an even larger diameter woofer, like an 18" and an even larger enclosure. The matching of a 15" driver with a 90° waveguide at 800 Hz seems to be, if not the ideal choice, certainly one of the few workable ones and optimal for a reasonable sized system. The smaller Geddes systems have to compromise on the above requirements, mostly at the crossover. As the LF driver and the waveguide gets smaller the crossover point must move upward and the control of the directivity become slightly less than the full size system. The Summa appears to be nearly ideal, but the Abbey is surprisingly close given its dramatically smaller size (and cost).
In order to be CD in all angles around the system (vertical and horizontal), the waveguide must be axi-symmetric, simply because the woofer is axi-symmetric. The waveguide will be found to require a mouth size that is exactly the same area as the 15" − which is not a coincidence. Smaller mouths do not allow the coverage pattern control down to the crossover point and a larger mouth would not offer a significant advantage. It is clear that for optimal performance in a small room the size and composition of the system components are not really a matter of free choice, but are dictated by the system requirements. Smaller enclosures require a compromise in system performance – most notably directivity control. Larger components might offer a slight advantage, but the current choice seems to be the best compromise – the sweet spot if you will.
Thank you guys for going through that revisit of polar matching =)...I wasn't getting the feeling on any emphasis on the idea that by "matching" polars we meant doing so by choosing different waveguides and woofers...its common sense, and a duh moment...but I would have worded it as "you have to choose a waveguide and driver combo that have a matching polar at desired XO"
Now I get to question every horn I've purchased lol
The strauss mf 2.1 uses the jbl 2380 with a 15"....I can't imagine they broke that rule...
My jbl 2386 seems to be made in an era when 15" mids were common
The 350hz e-tractrix has a width of about 12" before 1.5" roll over....
The Ev hp420....no idea but has a chance of being 15" friendly
No idea where the HvDiff fits in to this equation
Theres another horn that might steal the show if its design comes into fruition
And the show goes on. Right now, as said earlier, being able to cross lower via Axi, may be my saving grace in some of those scenarios.
Now I get to question every horn I've purchased lol
The strauss mf 2.1 uses the jbl 2380 with a 15"....I can't imagine they broke that rule...
My jbl 2386 seems to be made in an era when 15" mids were common
The 350hz e-tractrix has a width of about 12" before 1.5" roll over....
The Ev hp420....no idea but has a chance of being 15" friendly
No idea where the HvDiff fits in to this equation
Theres another horn that might steal the show if its design comes into fruition
And the show goes on. Right now, as said earlier, being able to cross lower via Axi, may be my saving grace in some of those scenarios.
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Here's a possible answers (from the attached paper):
The monopole generates two kinds of disturbances in the medium:
- Propagating sound wave radiating out from sphere
- Local flow- medium displaced radially by pulsations of sphere.
In the monopole, local flow vectors are aligned with sound propagation direction.
Two terms show up in the equation for radial particle velocity (r distance, U0 source velocity, k wave number).
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Or another scenario
There may be a horn profile that includes the 'best of all worlds':
- It is mathematically defined by a fairly simple equation, at least for an axisymmetrical horn.
- It contains a cutoff frequency.
- Coverage is almost perfectly controlled between < 500Hz - 10kHz.
- The throat area is as clean as possible.
Attachments
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