That sounds odd to me. Wouldn't both conditions produce the +3 dB increase? It amounts to two ways to double power.. When adding an identical thing gets a 6 dB rise, it's usually like adding a tape track or mixing two signals, on the basis that it's doubling the voltage. A second (and equal) combo wouldn't be doing this.
Anything more than 3dB extra from ganging driver arrays might be more to do with increased directionality from a wavefront that is wider at source, assuming they're closely set together and not cancelling at frequencies various due to mismatched distances.
Since you are using two amps, you get 6dB. The combined efficiency of two cabs is 3dB higher than one cab. You are also doubling to power which also gets you +3dB.
If you use only one amp to drive both cabs, it depends on how much power the amp produces at each impedance.
With a tube amp the power stays the same as long as the amp sees the expected load. So if the amp has a 4 ohm and 8 ohm tap it will make exactly the same power at either 4 or 8 ohms. Let's assume 100W and 8 ohm cabs with a
96dB 1W/1m sensitivity rating.
The decibel change from 1-100W is log(100) x 10 = 20dB. So one cab receiving 100W will make 96 + 20 =
116dB.
When you add the second cab, the total power remains at 100W, but it is divided equally between identical cabs. So each cab receives 50W. Since the power is cut in half, we know the SPL of one cab will drop by 3dB.
So each cab will make 113dB. Then you get +6dB from mutual summing and the total SPL is 113 + 6=
119dB.
Here is the math that shows each cab makes 96dB with 50W. Log(50) X 10 = ~ 17dB. This figure was rounded from 16.9897. The SPL of one cab receiving 50W is 96 + 17 = 113dB
We could look at it a different way:
Remember I said the combined sensitivity of two cabs is 3dB higher than one. This means as a system, the two cabs have a combined sensitivity of 96 + 3 = 99dB 1W/1m. 1-100W produces a 20dB change, so 99 + 20 =
119dB
Know we will show what happens with two 100W amps and two cabs. We already showed 1-100W produces a 20dB change and one cab will make 116dB with 100W. Since we have two amps, both cabs will receive 100W and make 116dB. So the total SPL will be 116 + 6 =
122dB.
Let's calculate this with 200W and the combined 99dB 1W/1m sensitivity rating. Log(200) x 10 + 99 =
122dB
Summary:
1 cab receiving 100W = 116dB
2 cabs receiving 100W total = 119dB
2 cabs receive 200W total = 122dB
I don't know the formulas for the mutual summing, but you can punch the figures into this online calculator:
Total dB level adding of coherent correlated sound sources
What's going on when you double the number of drivers. My understanding is increasing the effective radiation area of the speakers increase how effectively they couple with the air. In other words, efficiency goes up. You get near perfect summing for frequencies where driver spacing is less than 1/4 wavelength. Near perfect summing results in +6dB.
I believe this article probably gives a good foundational explanation:
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