# Calculating SPL of three identical speaker drivers in parallel

#### PeteHL

Joined Dec 17, 2014
475
Please tell me if you think that the following calculation is correct. The method is taken from a book on acoustics, but I've changed the given equations by applying them to sound pressure rather than sound intensity.

The three identical speaker drivers are connected in a parallel circuit and driven in parallel by an audio power amplifier. I'm considering the case where there is perfect summation of the sound pressure produced by each driver. The three connected drivers produce three times the sound pressure of a single driver which means that

Lsum = 20*log(3*Pd/ Pref)

where Lsum is the total SPL (dB 1W/ 1M), Pd is the pressure produced by a single driver, and Pref is the reference sound pressure. The above equation can be converted to

Lsum = 20*log(Pd/ Pref) + 20*log(3)

Given rated sensitivity of each driver equals 89 dB 1W/ 1M,

Lsum = 89 dB + 9.5 dB = 98.5 dB

The calculation is for the purpose of determining how effective placing three of the speaker drivers in a parallel circuit would be for the purpose of building a loudspeaker system of high sensitivity.

#### LowQCab

Joined Nov 6, 2012
4,071
Two Speakers = +3db, gain
Three Speakers = +4.5db, gain,
Four Speakers = +6db,gain.

This only applies to lower Frequencies and where the Cabinets
are separated by less than ~1/4 Wavelength of the highest Frequency of interest.

Higher Frequencies will start to create "Combing-Effects" in Frequency-Response
which will cause strange anomalies depending upon
where You are standing relative to the Speaker placements.

When placing multiple Speaker-Cabinets,
it is always advantageous to stack them vertically rather than lay them out horizontally.
This will promote more even Horizontal Sound dispersion, and better audience coverage.

Messing around with multiple Cabinets can be tricky business,
and the results are usually not very desirable,

If You need 3 Cabinets, You should replace them with single Horn-Loaded Cabinets.

What is your specific application ?
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#### PeteHL

Joined Dec 17, 2014
475
Two Speakers = +3db, gain
Three Speakers = +4.5db, gain,
Four Speakers = +6db,gain.

This only applies to lower Frequencies and where the Cabinets
are separated by less than ~1/4 Wavelength of the highest Frequency of interest.

Higher Frequencies will start to create "Combing-Effects" in Frequency-Response
which will cause strange anomalies depending upon
where You are standing relative to the Speaker placements.

When placing multiple Speaker-Cabinets,
it is always advantageous to stack them vertically rather than lay them out horizontally.
This will promote more even Horizontal Sound dispersion, and better audience coverage.

Messing around with multiple Cabinets can be tricky business,
and the results are usually not very desirable,

If You need 3 Cabinets, You should replace them with single Horn-Loaded Cabinets.

What is your specific application ?
.
.
.
For example, where two identical speaker drivers are driven in parallel by the same signal source, which is what I'm considering, then SPL of the pair is +6 dB relative to that of a single driver. I understand that if there is no correlation between the signals being reproduced by each of a pair of drivers reproducing in the same space, then the increase of SPL equals +3 dB.

My purpose is constructing a speaker system with sensitivity close to 100 dB 1W/1M.

#### BobTPH

Joined Jun 5, 2013
8,957
Your three speakers will use three times the power, the efficiency stays the same or decreases.

#### LowQCab

Joined Nov 6, 2012
4,071
What is the specific application ?
Indoor, or Outdoor ?
Home-Stereo ?
Live-Band, or Music ? ( PA or High-Fidelity ) ? ( Frequency-Response ) ?
Operation by clueless-Band-Members, or Experienced-Engineer, or Hobbyist ?
All information makes a difference.
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#### PeteHL

Joined Dec 17, 2014
475
Okay, well here are a few details for you to consider. I will be placing the speaker drivers as close together as possible to insure that the radiation centers of the drivers are not more than a wavelength apart within the frequency range that the drivers will be operated.

Now here is an equation (accepted by engineers!) that I didn't make up.

dB SPL = 20 log (P/Pref)

where P is the sound pressure produced by a driver and Pref is a reference sound pressure (threshold of audibility).

So let's say that you have two sound pressures P1 and P2, where P2 is twice P1, and we want to know what is the the difference of SPL of these two pressures P1 and P2.

dB difference = 20 log (P2/Pref) - 20 log (P1/Pref)

The above is equivalent to

dB difference = 20 log (P2/P1)

Further then, as P2= 2P1,

dB difference = 20 log (2)

dB difference = +6 dB

Granted I am considering an ideal situation where the pressure versus time of both drivers are exactly the same and that the pressures at any point in time add to make a total pressure that is double that of a single driver. But in reality it comes very close to the lossless addition of the pressures of the two drivers.

#### LowQCab

Joined Nov 6, 2012
4,071
Don't get too caught-up in Mathematical-Formulas and Theories,
they seldom work-out in the real-World the way that they would seem to indicate.

Single individual Speakers are available that exceed your ~100db goal.

Are You wanting to actually build something ?,
or are You just speculating for entertainment ?

Cabinet, and/or, Horn design are easily ~75% of the equation,
every part has to work together to perform well in a particular specified environment.

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#### PeteHL

Joined Dec 17, 2014
475
Don't get too caught-up in Mathematical-Formulas and Theories,
they seldom work-out in the real-World the way that they would seem to indicate.

Single individual Speakers are available that exceed your ~100db goal.

Are You wanting to actually build something ?,
or are You just speculating for entertainment ?

Cabinet, and/or, Horn design are easily ~75% of the equation,
every part has to work together to perform well in a particular specified environment.

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According to Vance Dickason in his cookbook, two drivers driven by the same voltage source and connected in parallel to the source increases measured SPL by 6 dB. Yes, I have a large number of one same driver that have been on the shelf for a number of years that I want to put to use. So this is a speaker system that I do intend to build at some point.

#### Audioguru again

Joined Oct 21, 2019
6,691
Vance Dickason is wrong. When in perfect identical phase, two speakers double the power which doubles the sound pressure by only 3dB.

#### LowQCab

Joined Nov 6, 2012
4,071
What is the Brand and part-number of the three Speakers that You have ?

What do You intend to use them for ?
You should probably use only 2 Speakers as a Stereo-pair,
and keep the third one for a spare, just in case.
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#### PeteHL

Joined Dec 17, 2014
475
What is the Brand and part-number of the three Speakers that You have ?

What do You intend to use them for ?
You should probably use only 2 Speakers as a Stereo-pair,
and keep the third one for a spare, just in case.
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The speakers are Aura model NS525-255-8A, 5.25 inch dynamic cone, 9 ohm. I have fourteen of them (!) that I bought about ten years ago I think for maybe \$1.50 each.

I was looking for a way to get them off the shelf and being put to use. A few months ago I was trying to sell most of my collection of drivers without much success. Also shipping costs for the individual currently I would say are steep.

My plan is to construct a pair of line arrays. Each speaker system will include six of the Aura driver, three of two drivers in series connected in parallel to the amp. So the pair will use up almost all of my stock and configured this way load presented to the amplifier is at a minimum of 6 Ohm.

#### Audioguru again

Joined Oct 21, 2019
6,691
Like most woofers, the 5.25" speaker produces cone breakup shrieking at 4kHz and 5kHz then a sharp dropoff of higher frequencies. So it needs a crossover at about 3kHz and a dome tweeter.

#### MisterBill2

Joined Jan 23, 2018
18,488
Here is another consideration: If the amplifier power output is the same for three drivers as it would be for one driver, then each of the three drivers in parallel would be getting only one third of the power. That would mean, probably, providing one third of the sound pressure, if perfect linearity can be assumed.
Of course, if the amplifier driving all three is adjusted to provide three times the power, then the case is rather different.
Another consideration is the area. given that pressure IS force per unit area, it is quite likely that physically putting three drivers in parallel will occupy an area greater than three times the area of a single driver.
Now a question about "Drivers", because the only drivers I am familiar with are made to couple to a horn of some variety. They consist of a voice-coil and diaphram followed by a chamber with an outlet port that will be coupled to a horn (trumpet) of some variety. So I am really wondering as to how these would be coupled in parallel.
Of course it is entirely possible that when the TS uses the word "drivers" that the meaning is totally different from that.
So an explanation of the word is very much in order.
And now, in the post#12, I see that AGA is using a term "speakers" in place of the word "drivers". I have NEVER heard loudspeaker devices called drivers.
This would be a classic example of the confusion created by speaking a different language.

#### PeteHL

Joined Dec 17, 2014
475
Like most woofers, the 5.25" speaker produces cone breakup shrieking at 4kHz and 5kHz then a sharp dropoff of higher frequencies. So it needs a crossover at about 3kHz and a dome tweeter.
What I have in mind is a crossover frequency equal to 2 kHz and crossing over to a horn tweeter with sensitivity 100 dB 1W/ 1M.

#### BobTPH

Joined Jun 5, 2013
8,957
And now, in the post#12, I see that AGA is using a term "speakers" in place of the word "drivers". I have NEVER heard loudspeaker devices called drivers.
People who sell raw speakers call them drivers to distinguish them from complete speaker systems. I have heard them called drivers many times, since I buy raw speakers and build speaker systems.

#### PeteHL

Joined Dec 17, 2014
475
Here is another consideration: If the amplifier power output is the same for three drivers as it would be for one driver, then each of the three drivers in parallel would be getting only one third of the power. That would mean, probably, providing one third of the sound pressure, if perfect linearity can be assumed.
Of course, if the amplifier driving all three is adjusted to provide three times the power, then the case is rather different.
Another consideration is the area. given that pressure IS force per unit area, it is quite likely that physically putting three drivers in parallel will occupy an area greater than three times the area of a single driver.
Now a question about "Drivers", because the only drivers I am familiar with are made to couple to a horn of some variety. They consist of a voice-coil and diaphram followed by a chamber with an outlet port that will be coupled to a horn (trumpet) of some variety. So I am really wondering as to how these would be coupled in parallel.
Of course it is entirely possible that when the TS uses the word "drivers" that the meaning is totally different from that.
So an explanation of the word is very much in order.
And now, in the post#12, I see that AGA is using a term "speakers" in place of the word "drivers". I have NEVER heard loudspeaker devices called drivers.
This would be a classic example of the confusion created by speaking a different language.
When I'm referring to a driver, I mean the device that converts the electrical signal to an acoustic one. Referring to it as a driver is better than referring to it as a speaker, because to many people speaker means a speaker system. Perhaps a better term would be speaker driver which I have used in this post, and then refer to driver as short for speaker driver.

#### Audioguru again

Joined Oct 21, 2019
6,691
A horn tweeter will be much louder (on axis) than a dome tweeter and the horn causes it to sound like a horn.
It will need attenuation to match the lower level of the woofer.

A woofer sounds "tight" (without resonances) when connected directly to the extremely low output impedance of a modern amplifier. Then three woofers in series are allowed to resonate and sound boomy like a bongo drum.

#### LowQCab

Joined Nov 6, 2012
4,071
These are reasonably high-performance, and reasonably High-Fidelity Speakers.
They are useful for Mid-Bass / Midrange usage only.

Since You have 9 of them,
I would recommend building a Corner-mounted 4-Woofer "Line-Array",
with your existing Tweeter mounted in the center of the 4.
and might let You get away without a Sub-Woofer for casual listening.

If You plan on pushing your luck with the Power and Bass-Frequencies,
a Crossover-Network that starts rolling-off the Low-Frequencies at around ~60hz will be required.
This Crossover can be Active, or Passive, or both,
using both is recommended for high-Power operation.

These Speakers will not reproduce Low-Bass Frequencies without damage at high-Power-Levels.
If You keep the power low, they will satisfactorily reproduce Low-Bass-Frequencies with lots of EQ.

Four 8-Ohm Speakers will allow a 2-in-series, plus, 2-in-series, connection
and will also double each Cabinet's maximum Power-Handling capabilities up to ~100-Watts RMS,
and also provide increased Efficiency, and Power-Handling by way of increased Cone-Area.

The 4 Woofers,
including the Tweeter which is mounted in the center of the Line-Array of Woofers,
should be spaced no more than around 1/2 inch apart.

The Tweeter should be roughly at "Head-Height" under the usual listening conditions.

The Cabinets should be Triangular in shape to fit tightly into the corners of the room.

For best Fidelity, including best "Transient-Response",
the Cabinets should be of Sealed-"Acoustic-Suspension" design and tightly packed
with "Rock-Wool" Building-Insulation, ( available at Home-Depot and Lowes ).

If You decide to go with Ported-Cabinets, you're on your own.
They will wind-up being "Boom-Boxes", with zero Low-Bass response.
I don't recommend this design for these Speakers.

A Sub-Woofer is highly recommended with these proposed Line-Arrays.
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#### Audioguru again

Joined Oct 21, 2019
6,691
The little speaker will be fine for an AM radio or for a speakerphone.

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#### MisterBill2

Joined Jan 23, 2018
18,488
The drivers that I have and have used all need to work with a horn arrangement of some variety. On the 100 watt variety, the entire diaphram is about 3 inches in diameter. And it has no cone coupled to the diaphram.
And when I say "Speaker System"folks all know what I mean.