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post #1 of 13 Old 07-15-2014, 10:50 AM - Thread Starter
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Total SPL produced

If I have 3 subs that produce say 96db each at 30 hz what would the total db perceived be?
...and how does the math work?
Thanks!
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post #2 of 13 Old 07-15-2014, 11:04 AM
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Quote:
Originally Posted by Plasmacolon View Post
If I have 3 subs that produce say 96db each at 30 hz what would the total db perceived be?
...and how does the math work?
Thanks!

googe yields http://www.sengpielaudio.com/calculator-spl.htm
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post #3 of 13 Old 07-15-2014, 11:07 AM
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Quote:
Originally Posted by Plasmacolon View Post
If I have 3 subs that produce say 96db each at 30 hz what would the total db perceived be?
...and how does the math work?
Thanks!

google yields http://www.sengpielaudio.com/calculator-spl.htm

but the room so controls response in the subwoofer frequencies that calculations are relevant, I suspect, only at a single frequency, and without measuring the SPL you get from each sub at any location in the room, you won't really know what you're adding
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post #4 of 13 Old 07-15-2014, 11:25 AM
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With the limited info given, this can't be answered. It would depend on if the subs were right next to each other, vs spread throughout a room, and the distance the the SPL was measured at. From 1 meter, or at the listening position.
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post #5 of 13 Old 07-15-2014, 12:06 PM
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+1 to all above.

In free space each additional point source would add 3 dB if the distances equal and all sources were independent and in phase at the measurement (listening) position. All those conditions are almost never satisfied in the real world.

In a room, especially at bass frequencies, it is impossible to say. You could even end up with less output using two subs if one sub cancels another. And since bass wavelengths are very long it is impossible to take the room (at least most practical rooms) out of the equation. In this case "the equation" being the Schrodinger Wave Equation (or Function as my prof defined it ages ago in a grad acoustics class).

"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
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post #6 of 13 Old 07-15-2014, 02:31 PM
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Quote:
Originally Posted by JHAz View Post
google yields http://www.sengpielaudio.com/calculator-spl.htm

but the room so controls response in the subwoofer frequencies that calculations are relevant, I suspect, only at a single frequency, and without measuring the SPL you get from each sub at any location in the room, you won't really know what you're adding

Let's remember that today people are setting up subwoofer systems that are flat within a few dB over the range of the subwoofers across large sweet spots. Obviously not everybody's system is that good, and it is also true that the output of some of the subwoofers is being traded off for that exceptionally smooth response.
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post #7 of 13 Old 07-18-2014, 04:50 AM
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Quote:
Originally Posted by DonH50 View Post
+1 to all above.

In free space each additional point source would add 3 dB if the distances equal and all sources were independent and in phase at the measurement (listening) position. All those conditions are almost never satisfied in the real world.
.
Not exactly

Assuming the following-1: All cabinets are the same and driven at the same level with the same signal.
2: All cabinets are within 1/4 wavelength at the highest freq of interest.
3: This is outside with no reflections that would cause cancellations and additions.

Will produce the following.

When you go from 1 cabinet to 2 you will get a 6dB addition.

To get another 6dB you need to go to 4 cabinets and another 6dB would require 8 cabinets .

You have to DOUBLE the number of cabinets to get the 6dB. It is real easy early on-but as the numbers get larger-they get REAL larger.

That is why you see so many subs at concerts-it takes more and more to get small gains.

So having a third cabinet would yield around a 3dB gain over 2 cabinets so 3 cabinets would be about 9dB louder than 1.

Yes the room can be a dominating factor (room modes).

Danley Sound Labs

Physics-not fads
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post #8 of 13 Old 07-18-2014, 06:00 AM
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I thought "independent" in my post implied 3 dB extra for each doubling in speaker count (for 4-pi space)? I did not assume they were within 1/4-wavelength. OTOH it has been a long time since I thought about this, and did not look it up in my old textbook, so I may well be wrong. The rest of your post makes sense, or at least jives with my foggy memory, so I am probably off... I assumed power factors (3 dB rather than 6 dB) for SPL doubling. Speaker design is NOT my area of expertise so I bow to your expertise!

Thanks - Don

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post #9 of 13 Old 07-18-2014, 09:18 AM
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Quote:
Originally Posted by DonH50 View Post
... I assumed power factors (3 dB rather than 6 dB) for SPL doubling.
A distortionless loudspeaker can be thought of as a linear system whose input is a voltage and whose output is the acoustic pressure at the location being considered/measured. SPL is defined as:

dB SPL = 20 * log10(|p / Pref|)

where Pref = 2 * 10^(-5) Pascals and p is the complex amplitude of the acoustic pressure (difference from atmospheric).

Say you're using Room EQ Wizard (REW) to individually measure the frequency responses of 4 subwoofers driven from the same mono source, using a properly functioning loopback timing reference in the REW measurement gear, with a single fixed measurement microphone position. You then get four plots of magnitude in dB SPL and phase vs. frequency for that mic position. The way you can calculate the summed output is as follows:

For each frequency:
  • For each measurement at this frequency, convert dB SPL + phase to a complex p / Pref ratio.
  • Compute the complex summation of the complex p / Pref values over all measurements for this frequency
  • Convert the complex-summed p / Pref from the previous step back to dB SPL and phase
  • Go to the next frequency and repeat the previous steps.
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post #10 of 13 Old 07-18-2014, 11:25 AM
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Duh, thanks Andy. 20 log, not 10 log... Pressure, power... Serves me right for depending on a 30 year old memory of a text instead of double-checking before I posted!

My apologies to Ivan Beaver, sir, you are quite correct (which I know you knew ).

Gotta' get my foot out of my mouth before I practice tonight! - Don

edit p.s. Andy, could you just RSS the magnitudes from REW then do 20log(RSS) to get a ball park? I don't use REW but assume it measures SPL like everything else...

"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley

Last edited by DonH50; 07-18-2014 at 11:30 AM.
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post #11 of 13 Old 07-18-2014, 12:58 PM
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Quote:
Originally Posted by DonH50 View Post
edit p.s. Andy, could you just RSS the magnitudes from REW then do 20log(RSS) to get a ball park?
I'm not sure how to answer that in a sensible way, except to caution that phase must be considered. Two equal-amplitude pressure waves that are 180 degrees out of phase at a single point in space give total cancellation at that point (in theory at least). An error of infinity dB is a big ballpark!

Quote:
Originally Posted by DonH50 View Post
I don't use REW but assume it measures SPL like everything else...
Implementation-wise, it measures a transfer function in the digital domain using a log-swept sine and FFT techniques. During the calibration part, it applies a pink noise signal and you measure it with an SPL meter and manually enter the meter's measured SPL value into a dialog box. After this, it calculates the scale factor to apply such that the magnitude of the measured transfer function corresponds to dB SPL.

For USB mics, there is a cal factor in the mic's cal file that it uses for this computation, and an SPL meter isn't needed.

Last edited by andyc56; 07-18-2014 at 01:09 PM.
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post #12 of 13 Old 07-18-2014, 01:37 PM
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I think you guys totally lost the OP with all this "log" "pref" and "pascals" talk.
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post #13 of 13 Old 07-18-2014, 02:39 PM
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@ andy: Yeah, right. I keep thinking of a different world where signals rarely add up. When they do we avoid them or launch something at them.

@ Alan P: Maybe, but it is useful info for others who might read and follow. As for me, I need to mess up in public now and again to keep myself honest. Of course, I could save myself the embarrassment if I want to know how stupid I am by simply asking my kids...

Pref = reference pressure
Pascal = unit of pressure

"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley
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