dB level of multiple speakers - Home Theater Forum and Systems - HomeTheaterShack.com

Old 09-25-08, 01:17 PM
Jokari
Inactive

Posts: n/a
dB level of multiple speakers

Hi,

I asked this question at the KVR forums, but no one had enough knowledge of acoustics or speaker design to answer. So here it is: say you have a passive speaker or subwoofer playing a low-frequency sound. Its acoustic output is 90 dB SPL at 1 m. Now add an identical speaker powered by a second identical amp right next to it. The acoustic level will be 96 dB SPL at 1 m, which is +6 dB higher, or in other words 4 times as much power. Obviously something special is happening, since you would expect two speakers to yield only twice as much power. Especially remarkable is that each speaker is now twice as efficient, since it is fed the same electric power as when it was alone (assuming its impedance didn't change) but it now outputs twice as much acoustic power. Because you could repeat this process with as many speakers as you'd like (you could stick 100 speakers together) and because the efficiency cannot be greater than 1, there has to be a limit to this phenomenon ; so speaker designers would have to pick an optimal number of speakers, above which there will be distortion no matter the sound level (!), and under which the efficiency will be reduced.

Is this correct? Do you have further reading related to this issue?

(PS: I wasn't sure what section to post this in. I first thought of "Home audio acoustics", but I settled for this section instead since the question is much more related to speaker design than to bass traps or acoustic treatment.)

Old 09-25-08, 01:46 PM
Bill

Join Date: Jun 2008
Location: New Hampshire
Posts: 185
Re: dB level of multiple speakers

The extra 3dB comes from mutual coupling, which occurs when identical drivers/speakers are placed within 1/4 wavelength of each other. Doing so doubles the radiating efficiency of the system with each doubling of the driver/speaker count. But is also lowers the high frequency region of flat response corner by a factor of 0.7 for each doubling, so there is a finite limit of approximately 25% radiating efficiency with direct radiating drivers, 50% with horn loaded.
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Old 09-25-08, 11:15 PM
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thxgoon

Join Date: Feb 2007
Posts: 1,506
Re: dB level of multiple speakers

Good post and good explanation! I've always wondered this too. So Bill, would the 25% finite limit also apply to subwoofers as they haven't much high frequency content?
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Old 09-26-08, 09:08 AM
Bill

Join Date: Jun 2008
Location: New Hampshire
Posts: 185
Re: dB level of multiple speakers

Quote:
thxgoon wrote: View Post
Good post and good explanation! I've always wondered this too. So Bill, would the 25% finite limit also apply to subwoofers as they haven't much high frequency content?
Yes.
Bill Fitzmaurice is offline
Old 09-26-08, 03:32 PM
Elite Shackster

thxgoon

Join Date: Feb 2007
Posts: 1,506
Re: dB level of multiple speakers

So despite manufacturer claims of multi-driver subwoofers, I guess there's only about a 4db advantage. Good to know!
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Old 09-26-08, 03:54 PM
Bill

Join Date: Jun 2008
Location: New Hampshire
Posts: 185
Re: dB level of multiple speakers

Quote:
thxgoon wrote: View Post
So despite manufacturer claims of multi-driver subwoofers, I guess there's only about a 4db advantage.
That's not what I said. For every doubling of driver count efficiency doubles, to a theoretical maximum of some 25%. Since the average sub has an efficiency of less than 3% that makes for a lot of potential improvement in sensitivity, at least 20dB.
Bill Fitzmaurice is offline
Old 09-26-08, 05:48 PM
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thxgoon

Join Date: Feb 2007
Posts: 1,506
Re: dB level of multiple speakers

I'm not sure you and I are on the same train of thought. You mean to say that if I put my subs next to each other, vs across the room from each other, I'll see a 20db increase in sensitivity??? Relating to the original posters question of how doubling drivers and power results in a 6db increase instead of 3db.

This theoretical max of 25%, I assumed that to mean that ideally you gain 3db from increased sensitivity, but in reality you only get up to about 25% of that.
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Old 09-26-08, 09:19 PM
Bill

Join Date: Jun 2008
Location: New Hampshire
Posts: 185
Re: dB level of multiple speakers

Quote:
thxgoon wrote: View Post
I'm not sure you and I are on the same train of thought. You mean to say that if I put my subs next to each other, vs across the room from each other, I'll see a 20db increase in sensitivity???
You will if you have enough of them. But that might be 16, might be 24, might be 32, depending on the driver's base efficiency, T/S spec No.
Quote:
Relating to the original posters question of how doubling drivers and power results in a 6db increase instead of 3db.
3dB from the doubling of power plus 3dB from the doubling of the driver count equals 6dB.
Quote:
This theoretical max of 25%, I assumed that to mean that ideally you gain 3db from increased sensitivity, but in reality you only get up to about 25% of that.
Doubling driver count doubles efficiency, which equals an increase in sensitivity of 3dB. But this process does not go on indefinitely. The highest possible efficiency is about 25%, with maximum sensitivity about 112dB/1 watt.
Bill Fitzmaurice is offline
Old 09-26-08, 11:01 PM
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thxgoon

Join Date: Feb 2007
Posts: 1,506
Re: dB level of multiple speakers

Quote:
Bill Fitzmaurice wrote: View Post
The highest possible efficiency is about 25%, with maximum sensitivity about 112dB/1 watt.
Ok, that makes sense. Thanks
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