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Author Topic: Cabinet addition and 'db' output.  (Read 1814 times)

Robin Whyte

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Cabinet addition and 'db' output.
« on: April 27, 2011, 01:08:07 pm »


Greetings ...

I asked a PA guy (who seems a bright fellow) at my local Sam Ash this question and I wanted to get a consensus on the answer.

Let's say I have a PA cabinet that is 8 ohms and a sensitivity of 95db per watt, a power amp with a LED output display and the world's greatest compressor.  I hook everything up, sing through my mic, and I get a perfect 1 watt of output at the amp.  I would expect I would get 95 db of beautiful 493.8 hz sound (the "She's Leaving Home" B) 1 foot away from the speaker.

Now let's say I hook up an identical speaker, in parallel, to the first one.  I sit them side by side so that 1 foot out from the center of both intersects.  I sing, 1 watt comes out of the amp.  What is the SPL at the "target" point of that 1 foot intersection?

Ok, I really love these speakers.  My amp run smoothly down to one tenth of an ohm in resistance.  I take two more of these speakers, put them in an arc, hook them up, sing, again get 1 perfect watt out of my amp ... what is the SPL at that 1 foot intersection?

Do the answers change if the speakers are hooked up in series versus in parallel?

TIA.

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Geoff Doane

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Re: Cabinet addition and 'db' output.
« Reply #1 on: April 27, 2011, 02:02:24 pm »

First off, I assume you mean 1m out from the speaker, not 1 foot (sensitivity specs are almost always given at 1W, 1m).

Once you hook up that extra speaker, your amplifier is now putting out 1W into each speaker, or a total of 2W.  Just that fact means that the total sound energy in the room is now 3 dB higher.  The amp really puts out a voltage, not power.  The impedance of the speaker(s) turns that into power.

And because the speakers are next to each other, not just pointing in random directions, you might get another 3 dB of level on axis in front of them (ignoring any room reflections).  So, if you're lucky, you might get another 6 dB, just by doubling the number of speakers (101 dB SPL in your example).  If luck is not on your side, you might be in a comb filter null, and the level could drop by 10 dB  :(.

GTD
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Robin Whyte

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Re: Cabinet addition and 'db' output.
« Reply #2 on: April 27, 2011, 04:53:09 pm »

First off, I assume you mean 1m out from the speaker, not 1 foot (sensitivity specs are almost always given at 1W, 1m).

Once you hook up that extra speaker, your amplifier is now putting out 1W into each speaker, or a total of 2W.  Just that fact means that the total sound energy in the room is now 3 dB higher.  The amp really puts out a voltage, not power.  The impedance of the speaker(s) turns that into power.

  (more deleted)

GTD


Hi GTD,

Yes, I meant 1 meter.  Sorry.

Also, electronics is not my thing - I was more a light guy in physics.  So, say the voltage - if that is what amps actually do - at the amp output does not change:  do I still then get 2 watts "post speaker" rather than one (and therefore two outputs of 95 db rather than one)?

Put another way, if I rephrase my question and say the voltage output of the amp stays the same, and I add a second identical speaker, is there a known formula that gives me the resulting increase in SPL?

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Brian Ehlers

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Re: Cabinet addition and 'db' output.
« Reply #3 on: April 27, 2011, 05:16:02 pm »


Put another way, if I rephrase my question and say the voltage output of the amp stays the same, and I add a second identical speaker, is there a known formula that gives me the resulting increase in SPL?
Yes.  Every time you double the number of speakers the SPL will increase 3 dB.  For what it's worth, while the amplifier is putting out the same voltage, it is now delivering double the electrical power, resulting in double the acoustic power, which is the same as adding 3 dB.  Of course, once you've got 8 speakers going, to add just another 3 dB you need a total of 16 speakers.

Please remember that all of this is theoretical and uses the simplest model.  It does not account for interference between the wavefronts produced by all these speakers nor room reflections.

If you don't like simply adding 3 dB and want to know the formula which produces that 3 dB, it's:
10*log(2/1)  where the (2/1) represents the doubling.  If you weren't doubling, replace (2/1) with the ratio of your choosing.  5 speakers compared to 4 would be 10*log(5/4) = 1 dB increase.
« Last Edit: April 27, 2011, 05:23:56 pm by Brian Ehlers »
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Ivan Beaver

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Re: Cabinet addition and 'db' output.
« Reply #4 on: April 27, 2011, 05:34:52 pm »

First off, I assume you mean 1m out from the speaker, not 1 foot (sensitivity specs are almost always given at 1W, 1m).

Once you hook up that extra speaker, your amplifier is now putting out 1W into each speaker, or a total of 2W.  Just that fact means that the total sound energy in the room is now 3 dB higher.  The amp really puts out a voltage, not power.  The impedance of the speaker(s) turns that into power.

  (more deleted)

GTD

Hi GTD,

Yes, I meant 1 meter.  Sorry.

Also, electronics is not my thing - I was more a light guy in physics.  So, say the voltage - if that is what amps actually do - at the amp output does not change:  do I still then get 2 watts "post speaker" rather than one (and therefore two outputs of 95 db rather than one)?

Put another way, if I rephrase my question and say the voltage output of the amp stays the same, and I add a second identical speaker, is there a known formula that gives me the resulting increase in SPL?


The the voltage stays the same the wattage will be doubled.  So you will gain 3dB from that.  You will also gain something else due to the additional radiation area of the loudspeakers.

It could be as much as 3dB or as little as no additional gain and actual lose of level.  It would depend on the particular freq involved and the differences in arrival times of the 2 cabinets and the combfiltering that is setup between them.

So it could be as much as 6dB greater or even 10dB or more quieter-depending on the freq involved.  And when you are talking a very specific freq-it could possibly be quite a bit less than 10dB quieter-if located in a cancellation notch.



« Last Edit: April 27, 2011, 07:08:31 pm by Ivan Beaver »
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Tim Weaver

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Re: Cabinet addition and 'db' output.
« Reply #5 on: April 27, 2011, 05:54:38 pm »

The answer to this, is as it so often is, it depends

When building speakers and you go from one woofer to two woofers that operate in the same frequency range you will get an extra 3dB of SPL if they are both playing the frequency range below which they become directional. For a typical 15 that would be somewhere from about 500hz and down.

If both of these woofers are being run from the same amp channel and they are wired in parallel, you would get another 3dB from the amp doubling it's voltage. If the woofers are wired in series you would get -3dB because the amp is seeing half the load and therefor it would halve the voltage.

So 2 woofers in parallel = +6dB, 2 woofers in series = 0dB net gain.

Why would anyone wire two woofers in series you ask? The power handling still doubles. You can now give the dual woofer section twice the power that you could a single woofer.


This scenario does not really hold true when you are talking about whole speaker cabinets. For the additive coupling to take place, both cabinets have to cover the same listening area with the same SPL coming from each cabinet. What's more, as the frequency rises most speakers become directional. You simply can't make 2 adjacent speakers cover the same acoustical space with perfect and even SPL.

More over as the wavelengths get smaller with rising frequency they will begin to combine in some areas and cancel in other areas. This is the concept known as "comb filtering".  So your combination of two adjacent speakers is not really adding up correctly at all frequencies. Typically the lows and low-mids will play the addition game, but the hi-mids and highs will be this lumpy soup of wishy-washy mess. Not what you want in the critical vocal range!

Then there are cabinets that are built to array properly. These will typically have really good pattern control so that each cabinet covers one small slice of the audience pie. At the point where they start to lose pattern control in the lower midrange they rely on coupling to the adjacent cabinets to bring that freq range back up to the nominal level of the array. If you looked at an untreated response graph of a big dog cabinet you might wonder why it looks so bass-shy. Thats because it is, until you add 6-12 of it's brothers alongside it.
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Re: Cabinet addition and 'db' output.
« Reply #5 on: April 27, 2011, 05:54:38 pm »


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