The acoustic summation of multiple drivers

[StigErik]

Lets assume we have four 15" drivers each with 90 dB / 2.83 V sensitivity, and we connect them in parallell. That should give an increase of 12 dB in voltage sensitivity, which is 102 dB / 2.83V

Now to the interesting point: is there any acoustic interaction between the drivers that gives us any more increase in sensitivity? I've seen claims from a speaker designer that we will get up to 3 dB additional increase in this case because of driver interaction.

Is this true, not true, or someway in between?

[ScottG]

Originally Posted by StigErik

Now to the interesting point: is there any acoustic interaction between the drivers that gives us any more increase in sensitivity? I've seen claims from a speaker designer that we will get up to 3 dB additional increase in this case because of driver interaction.

Is this true, not true, or someway in between?

It can be true.. but it isn't broad-band. Nor is it a set db figure.

Vance Dickson has this in his Loudspeaker Cookbook when using 4+ loudspeakers, often freq.s between 300 and 1.5 will receive some additional gain. An increase in drivers results in an increase in gain.

There are of course other factors like driver seperation distance, driver diameter vs. wavelength, etc...

[Paul W]

Doubling drivers (1 to 2) will gain 3db by doubling current/power delivery, 2 to 4 will gain another 3db, again by re-doubling the current/power. If there is close acoustic coupling, 1 to 2 will gain up to an additional 3db though increased radiation resistance, 2 to 4 can gain another 3db.

So, four drivers can deliver up to 12db through a combination of power delivery and acoustic coupling. Don't recall the driver spacing for full coupling, but I believe it is at/under a wavelength...think it is covered by Olsen etc.

[chris661]

Would it, by any chance, be when the speaker stops being a point source and becomes a plane/line source? These tend to have much greater sound projection than a single driver speaker, when they're both at the same level at 1m.

I'm no expert, but it hasn't been mentioned yet, so I figure I should put it into the melting pot.

[Rudolf]

Simply doubling the "baffle area" by positioning a second driver alongside the first will give you up to 1.5 dB. See my simulation in the diagram to the right (stig5.gif). Dotted line is for the added baffle.
Putting four drivers in a square could give +6dB - with still only one driver working. See how the on-axis response (upper line) is more affected than the power response - which was to be expected.

Another effect caught my attention: I simulated four drivers in the corners of a square with 2 m side length. Upper red line is the combined on-axis response, blue line same for a single driver, lower red line is the power response (second from left Stig3.gif).
(third from left Stig4.gif) is the same, but now with all drivers grouped closely together at 40 cm distance. On-axis response would not change in free space, but the power response would be raised by almost 5 dB at 100 Hz. So it would be a good idea to have those H-frames not too wide apart.

[john k...]

When discussing multiple drivers systems it is important to separate out the differences between efficiency and radiated SPL. For a multiple driver system where the drivers are acoustically close (much less than a wave length), assuming that each driver individually radiates the same SPL as if it were isolated, then the SPL is just the vector sum of the SPL form each driver. Being acoustically close means all drivers operate in phase so the SPL would increase by 6dB for two driver, 9.5dB for 3 drivers and 12dB for 4 drivers. This assumes also that the multiple driver system, is also small in dimensions compared to the wave length. (In other words, the radiation pattern remains spherical).

When looking at efficiency it is a simple matter of summing the input power. To keep the radiated SPL of each individual driver constant at the single driver level, the power delivered into the 2 driver system increases by 3dB, the three driver system by 4.77 dB and the 4 driver system by 6 dB. The the efficiency of the 2, 3 and 4 driver system increase by 3, 4.77 and 6dB as well. Or you cam look at it as the two driver system produces the same SPL as the single driver with 3 dB less power. The 3 driver system, the same SPL with 4.77dB less power and the 4 driver system the same SPL with 6dB less power.

Lastly, we should not confuse the effect of the baffle size on the SPL. It will produce the results the Rudolf indicates, but this is a result of the change in where the baffle related 2Pi tp 4Pi transition occurs, not changes is efficiency of the drivers.

[gedlee]

There are inter-driver effects, but they would best be described as 2nd order for 4 drivers. In a sonar torpedo head there were 256 individual transducers. At one location the inter-driver loading actually went negative at a certain frequency and blew up this transducer. Hence, in arrays of that complexity the effects can be significant, but with only four, its not really going to matter. That makes all the analysis above correct to first order.

[Rudolf]

After a nights sleep over the problem:
If you have some 15'' drivers to spend and we are talking of <200-300 Hz, you don't want to concentrate those drivers at one (or two) places. You want to distribute them WRT room modes. The advantage will be much greater than any possible gain for the clustered drivers.

BTW: Does anyone know, whether we can locate the below 200 Hz part of music (not sine waves!) for itself, when simultaniously hearing the part above 200 Hz from another location in the room? I'm not interested in individual observations, but scientific studies only. Do they exist?

Rudolf

[CLS]

What if the 'individual' is yourself?

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I'd like to recommend a perfect man (and his awsome system) for this experiment:
Large midrange for OB??? Scott G ?

However the re-config of such system must be very difficult....

[durwood]

See Jim Griffin's line array paper.

http://www.audioroundtable.com/misc/nflawp.pdf

Overall Array Sound Pressure Level and Impedance
The driver connections in a line array determine the overall impedance of the speakers
and connected to attain the resultant sound pressure level of the speaker. Individual
drivers are connected in series and parallel arrangements. For drivers that have sound
radiation patterns that overlap other drivers in the line there is a net increase in the
overall sound pressure level (SPL) results. For example, two speakers connected in
parallel and mounted within a wavelength center-to-center spacing would yield up to a 6
dB increase in SPL—3 dB from the increase in acoustical energy and 3 dB from the
reduction in impedance. Conversely, series connection of two speakers maintains the
same SPL of an individual driver but doubles the impedance of the pair. In a line array
various combinations of series and parallel connections can be used to give choices for
the overall impedance and SPL values.

The nominal impedance of a line array is computed by calculating the series and parallel
combination of impedances. That is, the impedance of each series connected branch is
added and then the parallel connections combined into the nominal impedance. Both
the acoustic response and the resultant nominal impedance of the overall system must
be considered.

While ultimately the SPL of the speaker will be measured, in the development process
you can compute the system sensitivity (or efficiency) impact of a line array. First,
assume that an individual driver in the line has a known SPL value. Next assume that
the drivers in the line have overlapping acoustical radiation patterns and are spaced
within a wavelength center-to-center from each other as stated in Table II. Thus, the
acoustical improvement (efficiency gain) at 1 watts, 1 meter distance is given by:

Efficiency Gain = 10*log (Number of Drivers Driven)

while the sensitivity gain or loss at 2.83v, 1 meter is:

Sensitivity Gain/Loss = 10*log (Nominal Driver Impedance/Nominal Array Impedance)

If the nominal array impedance is less than the individual driver impedance, the array
sensitivity increases or is a gain. If the array impedance is greater than the individual
driver impedance, then the sensitivity decreases or becomes a loss.
Hence, for the overall system

System Efficiency = SPL + Efficiency Gain
System Sensitivity = SPL + Efficiency Gain + Sensitivity Gain/Loss

In addition feel free to model in:

Vertical Polar Response: Line Array

The nice thing about arrays is they can work with the room when long enough.