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[Ivan Beaver]

OK I was wrong.  I was relying on my memory and stating up to 3dB difference.

It was actually a LARGER difference (at some freq).

Below is a screen capture of the array of 4 TH minis (top white trace) and some (not all) of the various endfire and "cardioid" arrangements that I did, below that.

As you can tell, there is quite a bit of difference.

These were all taken at the 0 point on axis-again about 67 feet away.  So that should be far enough away to negate most of the array depths.

[Tom Danley]

Hi Guys

There is some confusion about Ivan’s measurements and what is happening with these arrays.

When two or more sound sources like  subwoofers, of equal amplitude and phase are placed less than about a quarter wavelength apart, they feel the radiation pressure of the adjacent units and by mutual coupling are more efficient than a single unit would be.
In a perfect world, 4 identical subwoofers close together, would have 6 dB greater power handling AND 6 dB high sensitivity than one.
This effect is retained up to about 20-25% combined efficiency which is a practical limit for direct radiators.

Directivity?
The array above produces the same polar pattern as a single unit. The coherent addition in all directions results in a round (spherical) radiation or pattern.
A horn can raise efficiency and produce directivity but many do not realize that it is entirely different parts of the horn which are working doing each job even at a single frequency.
For example, for a typical HF horn, all of the impedance transformation takes place at the small end or even within the driver itself above 10Khz, while the other end is what governs pattern.  In other words, here the directivity generally is a result of the larger acoustical dimensions while acoustic coupling at small acoustic dimensions..

If one were to take two of the lf sources above and place them about 1 / 2  wl apart, then one finds the spacing is large enough to cause figure 8 radiation pattern broad side to the array.  In antenna theory these arrays are called “broadside arrays”, often made of many sources AND often tapered in amplitude and or phase towards each edge.
It was that tapering that made me try that in the Shaded amplitude horns fwiw.

If one has experienced the “power alley” effect, this is the experience being in that forward lobe, that same lobe also extends up and to the rear with nulls in line to the array.
Anyway, if you picture the ½ wavelength spacing it is easy to see why there is a figure 8 shape, on axis in line, you have two sources, a half wavelength apart so on axis, they will cancel out. Anywhere the path length difference is less than 120 degrees, the sources begin to constructively add (at 120 degrees, two sources add but have no increase).
Now, while a slice of this pattern looks like a figure 8, it is like a doughnut in 3d, where the in line nulls are the holes.
This produces a significantly different radiation pattern than the point source BUT one would note the spacing is too large to have the mutual coupling observed in the close coupled array.

Endfire arrays are another antenna configuration which is applied in audio.
Here one can picture the same array as the broadside except now one source is driven opposite the other. This rotates the strongest axis 90 degrees AND changes the shape of the beam    A very directional antenna can be made from a long row of sources each with the appropriate phasing and can often be made to project 90 degrees away by re-phasing

These types of arrays use local interference or they “self cancel” in some directions while adding in others, the sources are too far apart to add coherently like the close spacing does.

So what if you don’t want a rear lobe that is as strong as a front lobe?
Enter the time delay array or cardioid.

Take the two sources, place them physically a quarter wl apart (at or just past the limit for mutual coupling) and then add a phase difference via time delay which then kills the mutual coupling but produces a desired shape radiation lobe shape.

What Ivan had observed with his field measurements is correct, the greatest acoustic power would be produced by a close coupled array of the four units which add coherently, it doesn’t matter that these are Tapped Horns, it is the same for direct radiators.  
That would be especially clear if one were to integrate the power over 360 degrees, having less to the rear is accomplished by canceling some of it out with another source.
Thus the total radiated power is less than the sum of the radiated powers of source A and source B if they were adding coherently..

The issue would be how important is the radiation pattern VS how important is it to use the minimum cost / complexity..  With subwoofers this is can be a real problem as the total power needed can be large and this requires a lot of boxes and that means a physically large array which has physical directivity.

Conversely, for a given acoustic power, the desirable radiation patterns produced by local interference of sources comes at the expense of requiring more drivers, amplifiers , pounds of gear and processing.


Lastly, before running too far with this, we have to keep in mind how sound works to be realistic.  You cannot deal with sound in one plane except under a few circumstances, what looks like a row of sources conceptually in one plane, has to be a stack of them when you model height and width and wish symmetry.

Also, computer modeling is invaluable……but only to the degree it predicts what you actually measure in real life.
There is an increasing tendency in our industry to depend on modeling without any measurement backup.  Even some speaker EASE models are not actual measurements but models of the drivers in an array.
As a speaker designer, that is really a scary idea, I know of no software or collection of software I would trust enough to hang up the microphone.

This is the wrong way to look at things I think, a proper measurement trumps any computer model and what good is a computer model if it doesn’t predict the reality you construct from it?
It has never been easier to take good measurements, let those steer your way.
Anyway, some thoughts and Ivan’s parking lot test.
Best,
Tom Danley

[Bob McCarthy]

Most of what is stated in Mr. Danley extensive is understandable to me and fall in line with my experience.........but a couple of parts aren't and don't.

His advice to favor empirical measured data over predictions is wise. I have never found any prediction worth looking at that cannot be measured and found to be in close agreement. Suffice to say, I am a big fan of measurement.

1) the statement "The array above produces the same polar pattern as a single unit. "

I have never observed an array of speakers that produced the same pattern as a single unit. I don't see how such a thing is possible with even two displaced sources - much less four.  

2) the statements about 1/4 wavelength apart providing mutual coupling etc.....

In my measurements I have never seen "mutual coupling" show up on my analyzer screen as a special circumstance (i.e one where the combined behavior could not be deduced by the behavior of the individuals. What I mean by this is that I have never seen a break in continuity of behavior. If two sources are 120 degrees apart they "couple" just like two sources 120 degress apart, i.e. 0dB + 0 dB = 0 dB, which is to say it couples like a marriage between people who never see each other (half the folks in our field).  If they are 90 deg apart (the 1/4 wave distance), you get 3dB addition, i.e. better coupling.  91 degrees couples a little less than 3dB, 89 degrees a little more. Two sources, 90 degrees, or 89, or 60, or 30 degrees apart do not (in my experience of measurement) leave the pattern unchanged from a single source. The couple better (6dB) in the location where they are 0 deg apart - and they couple not so good (5.99999 down to 3 dB) in the direction where the displacement is maximum.

Maybe I am missing something, as I am not a theoretician. I don't do particle velocity, intensity, or wave theory. I can work a wrench but I am no quantum mechanic. I do amplitude and phase.

Here is what I do:
1) Measure speaker A (solo) - chart amplitude and phase
2) Measure speaker B (solo) - chart amplitude and phase
3) Compute expectations of A+B based on the solo data
4) Measure A+B and compare to expectations

To date I have never observed behavior that gave unexpected results (except when I screwed up something in my data acquisition).
To date the polar of A+B has never just been a louder version of A.

No disrespect is intended - I hope that is understood. I love that you guys took the time and expense to do these measurements. The results and conclusions just don't add up for me yet.  I would love to attend your next parking lot session.  I love to see the data going in.
Thanks

6o6  

[Tom Danley]

Hi Bob


"the statement "The array above produces the same polar pattern as a single unit. "

I have never observed an array of speakers that produced the same pattern as a single unit. I don't see how such a thing is possible with even two displaced sources - much less four."


Ah, your observation is correct, when I added the photo, it appeared in the beginning of the post instead of the end where the tag is.

I can see this would be confusing, as what I was saying referred to the closely grouped array in text above not the in line array shown photograph which appeared above.


"“In my measurements I have never seen "mutual coupling" show up on my analyzer screen as a special circumstance  snip>

Maybe I am missing something, as I am not a theoretician. I don't do particle velocity, intensity, or wave theory. I can work a wrench but I am no quantum mechanic. I do amplitude and phase.”


I'm a wrench guy too.

You described vector addition just fine that is how it is.


It is the radiation resistance curve which drive one to use a horn to increase the efficiency of a driver, when you examine such a curve for either a radiator or horn, one see’s that on the sloped portion, the efficiency goes up with radiator size.

The object of the horn then is to connect the driver which sits FAR down on the resistance curve, to be coupled to a point (ideally) where the radiation resistance is constant with frequency, without the mass a giant radiator that large would have.


When you take a small subwoofer, you are also very far down that curve, hence low efficiency but if you take two identical units and place them in close acoustic proximity, then, one finds the electroacoustic efficiency goes up by 3dB and combined with the 3dB you get from having twice the power handling, you get the 6 dB increase.

The closest thing to a free lunch in acoustics there is.

With direct radiators, there is a practical limit to the increase in efficiency somewhere around 20-25% where the wasted space between drivers and losses begin to limit.

Ref;

http://books.google.com/books?id=b_wxNccLhXoC&pg=PA78&lpg=PA78&dq=woofer+mutual+coupling&source=bl&ots=Kf8hiDxN9H&sig=RlyeqVubZnrUsvu_m3q6OWR6hcM&hl=en&ei=manMS5X_M4T2MMaeofsE&sa=X&oi=book_result&ct=result&resnum=4&ved=0CAwQ6AEwAzgK#v=onepage&q&f=false


Keep in mind, if your talking about acoustic power, it is only simple if you have an omni directional source like one too small to produce directivity, then one measurement point tells most of the story..    If you produce a polar pattern, acoustic power can only be assessed by a bunch of  spherical measurements, much more involved or measured in an appropriate reverberant room.


“I would love to attend your next parking lot session. I love to see the data going in.”


Well Mike, Ivan and Doug have talked about having some kind of fun / measurement seminar and maybe some sonic entertainment after dark for a while now.

They also have some great BBQ near the shop. 

So, it makes sense to mix Speakers BBQ, Measurements, listening to music.

Anyway, if that happens, you should come.

Best,

Tom Danley

Edit: link repair

[Greg Longtin]

Tom,

Tom Danley wrote on Mon, 19 April 2010 14:24

if you take two identical units and place them in close acoustic proximity, then, one finds the electroacoustic efficiency goes up by 3dB and combined with the 3dB you get from having twice the power handling, you get the 6 dB increase.

Some might just attribute that to coherent wave summing.

IOW, coherent is 6 dB, incoherent is 3 dB...

Greg

[Nick Hickman]

Two thoughts in response to Bob and Tom:

First, the principle of superposition (wave addition) will correctly predict the results of combining sources; there's no need to consider radiation impedance ("mutual coupling") as a separate issue.  Thus, predictions for everything from subs to line-arrays can be successful with simple superposition of sources.

Second, energy is always conserved.  If multiple sources are radiating sound energy, then all of that energy goes somewhere.  However, things are not always as straight forward as they may first appear, and issues of radiation impedance much be considered in order to see the whole picture.

In the hope it might help others following, I've found this thought experiment helpful in attempting to understand this ...

Take a small sub radiating at a low frequency into free space.  It's omnidirectional.  Integrate the sound power over space to find the sum of its output.

Now take a second identical sub driven in the same way with an identical amplifier and place it at a large distance (relative to wavelength) from the first.  We've added +3dB (double power) to the system by virtue of the second amplifier.  If we measure sound pressure, we find that it has increased +6dB in some directions relative to the first case but is greatly diminished in other directions.  If we integrate the sound power over space, we'll find it's +3dB.  Energy is conserved.

Now invert the polarity of one of the subs.  We find the pattern of peaks and nulls in the response will change but, if we integrate sound power over space, it's still +3dB.

Now restore the original polarity and slide the two subs so that they're right next to each other, closely spaced with respect to the wavelength of the sound.  We find that all the nulls in the response pattern that we had when the subs were widely spaced have now gone and, if we measure sound pressure, we have +6dB everywhere relative to the original single sub.  This is predicted by superposition.  If we integrate sound power over space, it's +6dB so, at first sight, it looks as if we've added 3dB to the system and got 6dB out.  But there has been another change: the radiation resistance into which both subs are radiating has been doubled by their effect on each other.  The effect of one sub on the other is making the air "stiffer" and enabling them to operate more efficiently.  Because the acoustic impedance is such a tiny part of the electrical load being driven by the amplifier, the change from the amplifier's perspective is small.

Last, invert the polarity of one of the subs while they remain close together.  The sound almost completely disappears and the power integrated over space is way down on the original case.  Again, this is predicted by superposition.  It looks like the energy has "cancelled" but, in reality, the subs' effects on each other is to radically reduce the radiation resistance by making the air "floppy".  As a consequence, little acoustic power ever gets delivered, and energy is conserved.

In all these cases, superposition predicts the result without any additional consideration of "mutual coupling".  To understand how this comes about with respect to the conservation of energy, however, it's necessary to consider the effect of mutual coupling on radiation impedance.

Nick

[Tom Danley]

Hi Greg, Nick

I could have explained things a bit more clearly in places.

One has to be careful where one applies general rules of physics, for example a first blush look at “conservation of energy” might suggest that adding two energy sources always results in more.  Active sound cancellation is based on having two equal but opposite sources which add ideally to zero .    
As Bob mentioned, it is magnitude and phase that govern the result when signals combine so no need to restate the obvious.

So far as mutual coupling, it is a real effect as is the radiation resistance curve.
The problem is, as soon as one has produced directivity, then one has eliminated the chance to determine the acoustic power with a single measurement like one can with a point source.

So, a thought experiments if you choose not to measure the real things.

Picture your in a huge and very live room.  
You place woofer A in the room playing noise in the spectrum of interest.
Given the surface area of the room and it’s absorption as well as the reverberant field sound level, one can calculate the acoustic power radiated by that speaker.

Now, add a second subwoofer NOT very close to the first and the reverberant sound level goes up 3dB, a factor of two which represents the doubling of source power.  

Place that second unit very close to the first and driven with the same power, the sound level in the room goes up 6dB over a single unit, representing the 3 dB you get from twice the power capacity and 3 dB or doubling if it’s acoustic efficiency because of mutual coupling / moving up on the radiation resistance curve.
Horns can be 10X or more efficient than direct radiators because of having a way to deal with that radiation resistance curve but when direct radiators are acoustically small, they show signs they follow along.

It is that coupling which makes the four close coupled subs, the most powerful acoustically (total acoustic power) while some of that power can be sacrificed for a more advantageous polar pattern.
Best,
Tom Danley

[Nick Hickman]

Hi Tom,

Tom Danley wrote on Tue, 20 April 2010 14:37

One has to be careful where one applies general rules of physics, for example a first blush look at “conservation of energy” might suggest that adding two energy sources always results in more. Active sound cancellation is based on having two equal but opposite sources which add ideally to zero .

Sometimes "cancellation" means there is no energy in the system, and sometimes it means that we don't see any energy because it went somewhere else or is in another form.  The "other form" arises because a sound field has a particle velocity component as well as a pressure component (what we hear).  Both fields must exist (over time and space) but it's quite possible to have velocity at a point and no pressure (or vice versa).

Take my example of two widely-spaced subs with inverted polarity.  You can put a pressure-sensitive microphone (or human ear) in the centre between the two sources and hear nothing.  There's no sound pressure, but there's still a velocity field (which can be detected with a velocity-sensitive microphone); the energy hasn't really gone away.

On the other hand, take the example of the two closely-spaced subs with inverted polarity.  You can put a pressure-sensitive or a velocity-sensitive microphone anywhere and hear nothing.  There's no energy because no energy was ever radiated.

Sorry if this takes things too far off track.  It's also taking me further out of my depth!

Nick

[Bob McCarthy]

I guess I am just a dyed-in-the-wool "superpositionist".  Two displaced speakers, two amplitude responses, two phase responses, one result (at a given location).

The Eargle reference Tom cited talks about "close together" and "tendency to act like a sinlge speaker".   I don't know what to do with this. What is close and how do I measure tendencies?

So much is made of 1/4 wavelength. But as I see it, it is just a milestone in our brains. The waveforms aren't checking for it.  If this "whatever effect" happens at 1/4 wavelength distance then what happens at 1/4 + 1/16th of a wavelength?  Or 1/4 less a 1/16th. If this event happens at 1/4 wave then what happens a 12th of an octave above or below? Something dramatic?  I have never seen a break in my data. I move the speakers an inch - the data moves an inch. I have never seen the fault line where some kind of transformation occurs.

Put two kids on a seesaw. The heavier kid sits on the ground and the lighter kid in the air - even if they are only different by a 1/4 pound.  The fulcrum of the seesaw is a transformational device. Give the skinny kid a dinner from KFC and we will see the fulcrum make a quantum shift.  I have not observed such a transformational device in the interaction of speakers.

Admittedly I don't use intensity probes so velocity and acoustic power are not in my vista.

I measure amplitude and phase with a single diaphragm mic. But I can (and do) put speakers right next to each other. In my expereience they never add 6 dB in all directions like people are saying here. The displacement pushes the phase responses apart by SOME amount in one plane - and along that line the addition is SOME amount less than 6 dB. Maybe a tiny amount... but the amount less than 6 tends to be consistent with the superposition principle.

I don't doubt the statements that my view is oversimplistic. But if somebody wants to give me a proceudure that I can use on my FFT analyzer to directly observe "tendencies to act like a single speaker" I will be happy to try them out.

Until then I will continue to do my best to avoid kryptonite

SuperpositionMan

[Nick Hickman]

Hi Bob,

As I wrote in the message you replied to, superposition predicts everything, so carry on being SuperpositionMan!

It's just that to fully understand the mechanisms at work behind the scenes, you must include changes to radiation impedance or you'll draw the incorrect conclusion that you're getting a free lunch in the form of more energy out than you put in.  (If not, why should moving boxes around change the amount of radiated energy?)  It's like attempting to compute a power change in an electrical circuit without accounting for a change in the circuit impedance.

Bob McCarthy wrote on Tue, 20 April 2010 18:46

So much is made of 1/4 wavelength. But as I see it, it is just a milestone in our brains.

Yes, absolutely.  Everything is gradual; no sharp boundaries.

Quote:

But I can (and do) put speakers right next to each other. In my expereience they never add 6 dB in all directions like people are saying here. The displacement pushes the phase responses apart by SOME amount in one plane - and along that line the addition is SOME amount less than 6 dB. Maybe a tiny amount... but the amount less than 6 tends to be consistent with the superposition principle.

Yes!  If the sources were truly co-located (which is impossible in the real world), you'd get +6dB, as predicted by superposition.

Nick

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