multiple speakers and SPL

[eschertron]

I have a problem with their description of the test design. Are the cabinets in the same plane? If so, then the mic is off axis to both speakers and I 'd expect some wavefront coupling where the response was dropping from either speaker alone. Are the cabinets arrayed so that they point -directly on-axis - at a microphone 1m from each? If so, I'd expect a frequency coupling that is observed (as when) placing a cabinet next to a wall, essentially defeating the anechoic chamber thing. And 1m distance? Not a viable test of audience perception.

Not that I've made up my mind about the discussion. I know from reading my freshman physics book Principles of Physics, Hurley & Garrod that for a point source (spherical, or three-dimensional dispersion), the amplitude is inversely proportional to the distance. For a cylindrical source (two-dimensional dispersion), amplitude inversely related to the square root of the distance. For a planar wave(one dimension), amplitude is constant. Any real-world anecdotal or empirical evidence will necessarily be close to, but exactly, one of these situations. Even without extra factors such as reflections, interference, standing waves, etc. etc. compromising the data.

I believe that if the listener is close to the source, the source approximates a planer source. The authors of the text describe this in a thought experiment with a infinitesimally small sample of air extremely close to a piston source, so that all the air molecules are moving in perpendicularly to the piston face. That's me, sticking my head in front of the speaker looking for the 'sweet spot'. If the listener is sufficiently far from the source, the amplitude (SPL) at the listener has fallen by as much as 1/distance. Adding a second speaker improves the result simply because the speaker/listener system has incrementally approached the planar model, by however little amount. And as the listener gets closer to the source, any change to piston area becomes more important.

...so back to the experiment: put the mic far away from the speaker(s) and run the test again.

[J M Fahey]

Oh dear, of course, the post is from user id GT100

Thanks a lot

Result is interesting, still I find it incomplete.

My main beef is still with "increasing efficiency", specially *doubling* it .

Yes, curves show around 3dB difference in SPL at the microphone position.

Which does not mean doubled efficiency but , as I see it, *focusing* , for lack of a better word.

Also microphone distance is way too small compared to voice coil to voice coil distance, so speaker source can NOT be considered a point source by any means.

As mentioned above, at such close distances wave dispersion is way closer to cylindrical or even flat/planar , not "point source spherical" by any means.

Again, I suspect SPL increase on axis will be accompanied by equivalent decrease at, say, 45 degrees .

My experiment will basically be:
1) measure 1 speaker at, say, 4 or 5 meters away, simply to still have close to point source when adding the second one.
2) adding second speaker, touching the first one edge to edge, plus twisting it a small angle so it also points straight at the microphone
3) measuring on axis with 1 and 2 speakers, then repeating 45 degrees away.
4) obviously I have everything needed, including a Lab quality RION SPL meter, BUT no anechoic room, and being in a compact City walls everywhere.
Will try to do the experiment at night or, say, early Sunday morning, at some nearby Public square or 100 meters away at the River edge, only problem is where to get 220V mains nearby, specially in the wee hours.
Plus neighbours will hate me
I think with speakers far enough to be considered a point source, (and using a more typical Club speaker-to-listener distance) and also measuring at 45 degrees I´ll be able to back either the increased efficiency or beaming theories.
Again, "doubling efficiency" out of the blue scratches me the wrong way, I don´t see (nor anybody offers) any physical explanation for that.

[HaroldBrooks]

I would like to see the results of your proposed test Mr. Fahey, it sounds like a very good one. It's a complex interaction between a single speaker and a listener, much less two speakers, so it may be fair to say that no single measured parameter will address the differences in total.

I'll make a guess that with either too little wattage into multiples speakers (in the low millivolt watt), or too much wattage into one speaker, there will be problems with the efficiency of either setup vs. the other, respectively, and I would also think some law of diminishing returns would apply with multiple speaker setups and the perception of loudness, particularly if you stand in the wrong location or if the speakers are not properly aimed and coupled in a manner complimenting the frequencies to be tested.

Then there is the perception of the 'size' of the sound source that would be thrown into the mix, and would probably affect judgment of overall volume. After all, measurements would only be useful if there was a human perception of change in loudness, IMHO.

Oh, and some of the neighbors will hate you no matter what, so give them a real reason !

[potatofarmer]

Again, "doubling efficiency" out of the blue scratches me the wrong way, I don´t see (nor anybody offers) any physical explanation for that.

Would you feel better if it were phrased as "doubling sensitivity?" If one transducer with 2.83 V input can produce 100 dB SPL as measured 1 meter away, then 2 of that particular transducer would (theoretically) produce 103 dB SPL measured the same way.

Talking about coupling effects, phase interactions, etc. all seems a little beyond the scope when we're only talking about the drivers as "8 ohm nominal," or whatever. I'm sure some of the more advanced modeling software packages could answer this question down to the effect of temperature in the room on voice coil temperature rise.

[printer2]

Hope this goes well. I was part of the same kind of discussion at tdpri years ago and I said that the power remains the same so therefor the spl does also. But I had no real world experience to back it up. So I did a test. I hooked up a pair of 15's in seperate cabinets, Yamaha 2200 amp, signal generator, voltmeters on the outputs, spl meter. Took pictures of it all at each step showing the spl meter beside the volt meters showing the applied voltage with a one watt level being the applief power.

One watt of sine wave power is loud, even with muffs. I was wrong, there was a 3 dB increase in spl. I thought about the increased surface area and increased acoustical impedance transfer as what happens with horns. It seems to work. Why can you not add speakers to get to infinity with one watt? It has to do with wavelength. As you approach the wavelength each time you double the speaker area you get a fraction of the 3 dB increase.

So in my test how could I be sure it was not just a standing wave from two sources at a particular frequency? I swept it through a range with no change in increase. Years later the same discusion came up, I pointed to my test, one poster said it must have been a standing wave and I should have used a multifrequency noise source. Just to get rid of that argument I redid the test with white noise from a FM recieiver tuned between stations. Did the test and photographed the results. Same deal, 3 dB increase for the same power level. When I get home I will try to find the thread with the results.

Found one thread.

http://www.tdpri.com/threads/running-two-15-watt-amps.355755/page-2

[eschertron]

Would you feel better if it were phrased as "doubling sensitivity?" If one transducer with 2.83 V input can produce 100 dB SPL as measured 1 meter away, then 2 of that particular transducer would (theoretically) produce 103 dB SPL measured the same way.

Good question. If one "8 Ohm nominal" driver has 2.83v applied across it, then adding a driver (and matching the impedance from the OT) will result in some voltage less than the 2.83v (.707*2.83v in theory) applied to each driver. What does the driver's sensitivity measure then?

[J M Fahey]

Why can you not add speakers to get to infinity with one watt?

That´s exactly my point.
No need to get to infinity, just very doable 8 speakers , 2 plain vanilla 4 x 12" stacked should melt your brain, literally, we would be talking 9dB increase, almost 10:1 .
2 stacks side by side would be immense 12dB.
But I have heard them countless times, loud as hell but didn´t turn 100W into 1584W by any means.
Yet that´s a 12dB ratio.

It has to do with wavelength. As you approach the wavelength each time you double the speaker area you get a fraction of the 3 dB increase.

Well, maybe.
Not going one way or the other until experimenting.

So in my test how could I be sure it was not just a standing wave from two sources at a particular frequency? I swept it through a range with no change in increase. Years later the same discusion came up, I pointed to my test, one poster said it must have been a standing wave and I should have used a multifrequency noise source.

Notice I fear a lot about standing waves pollutig results, that´s why I want to experiment in a public square or at the river side.
Would prefer the middle of the Country and even better hanging speakers from a pole a few meters fron the ground (what they used before anechoic chambers were available) but let´s be realistic.
And in principle I will use pink noise.

Just to get rid of that argument I redid the test with white noise from a FM recieiver tuned between stations. Did the test and photographed the results. Same deal, 3 dB increase for the same power level. When I get home I will try to find the thread with the results.

Thanks.

[nickb]

That´s exactly my point.
No need to get to infinity, just very doable 8 speakers , 2 plain vanilla 4 x 12" stacked should melt your brain, literally, we would be talking 9dB increase, almost 10:1 .
2 stacks side by side would be immense 12dB.

It's ideally 9dB not 12dB. 2 speakers = 3dB, 4 speakers =6dB, 8 speakers =9dB. Still it does stretch credibility.

I don't think the Celestion results told us very much as there was no distinction between mutual coupling effects and beamforming.

Notice I fear a lot about standing waves pollutig results, that´s why I want to experiment in a public square or at the river side.
Would prefer the middle of the Country and even better hanging speakers from a pole a few meters fron the ground (what they used before anechoic chambers were available) but let´s be realistic.
And in principle I will use pink noise.

Thanks.

I'd expect anechoic results from this to confirm beamforming, meaning many measurements need to be made at differenct places, say around a circle in a plane that is parallel to the that of the speakers ans whose centre on the in speaker mid-point axis. The paper was very clear that a reverberant environment is required to get mutual coupling.

I look forward to results from a properly designed experiment.

[J M Fahey]

It's ideally 9dB not 12dB. 2 speakers = 3dB, 4 speakers =6dB, 8 speakers =9dB. Still it does stretch credibility.

I said 9dB with 8 speakers, and 12dB with 16 ("2 stacks side by side")

Quote Originally Posted by J M Fahey View Post
No need to get to infinity, just very doable 8 speakers , 2 plain vanilla 4 x 12" stacked should melt your brain, literally, we would be talking 9dB increase, almost 10:1 .
2 stacks side by side would be immense 12dB.

[printer2]

That´s exactly my point.
No need to get to infinity, just very doable 8 speakers , 2 plain vanilla 4 x 12" stacked should melt your brain, literally, we would be talking 9dB increase, almost 10:1 .
2 stacks side by side would be immense 12dB.
But I have heard them countless times, loud as hell but didn´t turn 100W into 1584W by any means.
Yet that´s a 12dB ratio.

I am wondering how much gain a horn loaded cabinet provides? Same idea in trying to get the best impedance match to the air with going to multiple drivers. 130 dB, I have been in front of PA's that sounded like it, never had a real loud band to work with playing the bars so I could not say.

[The Dude]

The purpose of the horn load is focus and distance. Design will dictate how loud, how far, on-off axis (pattern) , etc. You're asking a loaded (no pun intended) question.

[pdf64]

Thanks a lot

Result is interesting, still I find it incomplete.

My main beef is still with "increasing efficiency", specially *doubling* it .

Yes, curves show around 3dB difference in SPL at the microphone position.

Which does not mean doubled efficiency but , as I see it, *focusing* , for lack of a better word.

Also microphone distance is way too small compared to voice coil to voice coil distance, so speaker source can NOT be considered a point source by any means.

As mentioned above, at such close distances wave dispersion is way closer to cylindrical or even flat/planar , not "point source spherical" by any means.

Again, I suspect SPL increase on axis will be accompanied by equivalent decrease at, say, 45 degrees .

...with speakers far enough to be considered a point source, (and using a more typical Club speaker-to-listener distance) and also measuring at 45 degrees I´ll be able to back either the increased efficiency or beaming theories.
Again, "doubling efficiency" out of the blue scratches me the wrong way, I don´t see (nor anybody offers) any physical explanation for that.

Yes, my understanding (simplistic / layman variety ) is that the +3dB is in regard of 'forward' efficiency and comes at the expense of a corresponding lowering of SPL around the sides; so better 'focus' but the overall sound power remains the same.

The issue is phase cancellation between drivers; for mega arrays (eg the double full stack 16x12 mentioned), that will probably result in a multiple comb filter effect, which will degrade sound quality and increasingly negate any forward benefit. So a rapidly diminishing return as the array doubles.
It was a long time ago, plus I'm not sure all drivers were the same model, but when I've plugged into an amp with 2 x Marshall 4x12 cabs side by side, the tone had a somewhat 'diffuse' quality that seemed to reduce the brutal impact I expected from the rig.

'Beaming' is probably best seen as a different thing, though the 'focus' of the beam does seem to be intensified by a close, aligned array.

[printer2]

Getting rid of theory, so what does that give us in real world conditions? How much gain in dB will we see in the low end of the operating spectrum on axis? And given an array of drivers in a non-loaded cabinet what would be the dB gain for a comparable wavelength to surface area as compared to a horn enclosure? Is the dB gain a function of the directivity or is it due to better acoustic loading? I looked up horn loaded cabinets to get their SPL at 1W figures and wanted to find out the driver's SPL figure alone but it is a more daunting task than you would think.

And then about beaming, I did my testing with a floor and wall position for the speakers in a room. I also used frequencies low enough for directivity to not come into play and still saw the same rise in dB.

[Malcolm Irving]

As a thought experiment, imagine a speaker working into a vacuum - there would be no acoustic power output at all. The speaker would get a bit hotter, because the small amount of energy that usually goes into sound would now just be 'reflected back' into the speaker to create extra heat.

A speaker needs 'something to push against' to do work on the air (i.e. transfer energy from the cone to the air).

If we have 2 speakers and they are close together (relative to the wavelength of the sound) the air at the surface of each cone is already pressurised by the sound from the other speaker - giving each speaker more to push against.

When the cones are moving the other way, each speaker has 'more to pull against' due to the sound wave from the other speaker.

[Helmholtz]

As a thought experiment, imagine a speaker working into a vacuum - there would be no acoustic power output at all. The speaker would get a bit hotter, because the small amount of energy that usually goes into sound would now just be 'reflected back' into the speaker to create extra heat.

A speaker needs 'something to push against' to do work on the air (i.e. transfer energy from the cone to the air).

If we have 2 speakers and they are close together (relative to the wavelength of the sound) the air at the surface of each cone is already pressurised by the sound from the other speaker - giving each speaker more to push against.

When the cones are moving the other way, each speaker has 'more to pull against' due to the sound wave from the other speaker.

Excellent!

That's exactly how Prof. Zollner explains the phenomenon in his book "Elektroakustik für Bühne und Studio".

My interpretation:

A speaker is like a motor running almost at idle, not having an appropriate load. Consequently its power efficiency is low. Increasing the load increases efficiency.

Acoustic speaker impedance is much higher than that of the surrounding air and typical guitar speaker efficiency is only around 3%.
Its electrical equivalent would be a high impedance (current) source driving a low impedance load. This configuration doesn't allow to couple much power. Increasing the load impedance increases power efficiency until the load impedance equals the source impedance. Also meaning that efficiency/power gain must progressively decrease with higher load impedance (or speaker number).

Acc. to Zollner the effect was already described and explained in 1960 by R. Pritchard : "Mutual Acoustic Impedance....", JASA 32, 1960, pp. 307-377.