Sensitivity of multiple drivers?

[Snickers-is]

If I have a lot of woofers with the following parameters:

8 ohms (flat)
100dB@1W/1m.

Then I connect two i paralell, and I get 106 dB@2,83 volts.

Then I connect anoter pair in series with the two. Then i get back to 8 ohms, but with still 106dB@2,83 volts.

Then I connect another four woofers in paralell, and then another 8 woofers in series we should have 112dB@2,83 volts and still 8 ohms.

If we go on with another 16 woofers in paralell and another 32 in series we are at 118 dB@2,83 volts. And on and on and on.

But if we had 1,2677E+30 drivers (a relatively large and expensive speaker) and connect them the same way. We should have about 400dB@1W/1m.

This does not make sense to me, but wat is actually wrong in the theory?

[Pan]

"But if we had 1,2677E+30 drivers (a relatively large and expensive speaker) and connect them the same way. We should have about 400dB@1W/1m."

400dB@1W/1M is serious overkill... big time..

I would settle for a more sane figure of 200dB@1W/1M or so..



/Peter

[Snickers-is]

A little hard to explain to the ensurance company that you have blown away the neighbourhood testing a 1W amplifier.

[bwbass]

I think you'd hit some point of diminishing returns where the meager power you're putting into the system is dissipated as low level heat due to resistance in the thousands of miles of wire it's going through.

Also 1/(1,2677E+30) watt in any one driver probably won't be enough to overcome the internal friction involved in moving the spider/suspension out of it's resting position. Starting friction is always greater than moving friction, they say, and I would assume this would apply to moving the cone of a driver from rest (stopped).

All of these factors would eat away at effiency of a Very Large Array speaker like this when the number of drivers passes a certain point... This seems like a really fun thing to figure out with limit theory, but I don't think I'm up to the math.

[joe carrow]

I was thinking about this not so long ago, and it occured to me that when you get such a large number of drivers, the wavelength of the sound would start to get in the way of using them all together. So, it would depend on their configuration and the desired bandpass.

I read here that an acoustic watt is equivalent to an SPL of 109 db at one meter, radiating spherically; therefore it's impossible to have something that produces more than 109 db from one watt in an omnidirectional pattern. Of course, some horns are over 109 db/watt/meter- but their radiation pattern is far from spherical.

Perhaps somebody with more knowledge about the equations used can let us know what the true relationship is between radiating surface area and efficiency. It's a log scale, and 3 db/doubling is really only a rule of thumb that applies over a certain range. Don't forget that when you're talking about efficiency, 100% is 100%

[bwbass]

I read here that an acoustic watt is equivalent to an SPL of 109 db at one meter, radiating spherically; therefore it's impossible to have something that produces more than 109 db from one watt in an omnidirectional pattern.

True, though I think a super-array like this would have a quasi-planar radiation, since with any reasonable sized driver the array would be larger than the longest audible wavelength. You'd get something like "high-frequency" beaming from the array at all audible wavelengths. I would think the acoustic dropoff with distance would be different, in this case.

[DavidH]

Originally posted by Snickers-is
Then I connect anoter pair in series with the two. Then i get back to 8 ohms, but with still 106dB@2,83 volts.

Hi, Snickers-is. A fun idea.

I think the above sentence is the flaw. You get back to 8 ohms, and also back to 100dB.

By adding the series speaker you are potentially adding 6dB in total, but now each speaker is receiving half power, so EACH speaker is producing 6dB less. So the effect is 'plus 6dB' and 'minus 12dB', for a net loss of 6dB, back down from 106dB to 100dB.

Regards ... /Dave

[murat]

Once you put two speakers in series and apply 2.83V, this voltage will be divided into two: 2.83/2 = something smaller.

Power = V^2/R (assuming ohmic resistance for simplicity)

These two points above is in principle enough to figure out what is going on with 1,2677E+30 drivers and resolve the paradox. Cheers,

Murat

[Svante]

Originally posted by Snickers-is
If I have a lot of woofers with the following parameters:

8 ohms (flat)
100dB@1W/1m.

Then I connect two i paralell, and I get 106 dB@2,83 volts.

Then I connect anoter pair in series with the two. Then i get back to 8 ohms, but with still 106dB@2,83 volts.

Then I connect another four woofers in paralell, and then another 8 woofers in series we should have 112dB@2,83 volts and still 8 ohms.

If we go on with another 16 woofers in paralell and another 32 in series we are at 118 dB@2,83 volts. And on and on and on.

But if we had 1,2677E+30 drivers (a relatively large and expensive speaker) and connect them the same way. We should have about 400dB@1W/1m.

This does not make sense to me, but wat is actually wrong in the theory?

The error is that the formula assumes that the motion of the cone is mass-controlled. If you add a sufficient number of drivers, the radiation resistance finally dominates the mechanical impedance, and the efficiency flattens out towards something less than 100%.

Another way of looking at it, is that the model assumes that the cone motion of the individual drivers remain the same as you add more and more speakers. In the real world, given a sufficient number of drivers, the sum of their sound pressures reduce the movement of the cones. Again, this limits the efficiency to something less than 100%.

[simon5]

Another problem in this formula is that you can't add too much drivers or you lose the efficiency advantage.

Let say we want to reproduce a 10 kHz sinewave, we have a wavelength of about 3,4 cm. Even with 2.5 cm tweeters, using the pythagore formula and standing about 4 meters from the center of the baffle, let me do a triangle... If we know that at 4,017 meters from the side of the baffle, the tweeter will be out of phase. We have less than 37 centimeters maximum on each side before going out of phase with the listener. That means to get absolutely no cancellation, we need to stay under 18 cm per side so a baffle of 36 cm wide total.

Let say with something bigger than a 14x14 array of 2,5 cm tweeters, I guess you'll get cancellation with drivers being out of phase according to the listening position, so decreasing total efficiency.

But, a 14x14 array of tweeters should give at least a 110 dB / 1W / 1m ?