When you double matching cabs in parallel: sensitivity goes up +3dB, power handling doubles, impedance is cut in half.
The sensitivity gain assumes perfect summing. Real world gain will be slightly less; perhaps 2-2.5dB
Example:
Ampeg 810E
Sensitivity = 100dB 1W/1m
Power Rating = 800W
Ampeg 410HE. Same drivers but the internal chambers are slightly smaller.
Sensitivity = 98dB 1W/1m
Power Rating = 500W
Calculated SPL = [Log(usable power) x 10] + sensitivity at 1W/1m
FYI the part of the equation in brackets calculates the decibel change from raising to power from 1W to the usable power.
If power is held constant, the difference between these cabs will be 2dB per the specs, because the 810 has a 2dB higher sensitivity rating.
At 300W
810 = [Log(300) x 10] + 100 = ~124.8
410 = [Log(300) x 10] + 98 = ~122.8
As you see, calculated SPL for the 410 is +2dB.
Decibel change 1W to 300W = [Log(300) x 10] = ~24.8dB
In order for the 410 to play as loud as the 810, you need 2dB more usable power.
Solve for 2dB increase over 300W.
I'll insert images of the math as I don't think you can write the formula directly here.
Convert to exponential
Solve for X
Let's confirm with the Log form
Decibel Change 300W to 475.5W = Log(~475.5/300) x 10 = 2dB
Calculated SPL of 410 at ~475.5W = [Log(475.5) x 10] + 98 = 124.8dB
Theoretically a 410 with ~475.5W should play as loud as an 810 with 300W. However, the 410 is running pretty close to it's 500W power rating, so you will probably loose a bit of SPL to power compression. The 810 will experience less power compression because it is running at < half of rated power.
The sensitivity gain assumes perfect summing. Real world gain will be slightly less; perhaps 2-2.5dB
Example:
Ampeg 810E
Sensitivity = 100dB 1W/1m
Power Rating = 800W
Ampeg 410HE. Same drivers but the internal chambers are slightly smaller.
Sensitivity = 98dB 1W/1m
Power Rating = 500W
Calculated SPL = [Log(usable power) x 10] + sensitivity at 1W/1m
FYI the part of the equation in brackets calculates the decibel change from raising to power from 1W to the usable power.
If power is held constant, the difference between these cabs will be 2dB per the specs, because the 810 has a 2dB higher sensitivity rating.
At 300W
810 = [Log(300) x 10] + 100 = ~124.8
410 = [Log(300) x 10] + 98 = ~122.8
As you see, calculated SPL for the 410 is +2dB.
Decibel change 1W to 300W = [Log(300) x 10] = ~24.8dB
In order for the 410 to play as loud as the 810, you need 2dB more usable power.
Solve for 2dB increase over 300W.
I'll insert images of the math as I don't think you can write the formula directly here.
Convert to exponential
Solve for X
Let's confirm with the Log form
Decibel Change 300W to 475.5W = Log(~475.5/300) x 10 = 2dB
Calculated SPL of 410 at ~475.5W = [Log(475.5) x 10] + 98 = 124.8dB
Theoretically a 410 with ~475.5W should play as loud as an 810 with 300W. However, the 410 is running pretty close to it's 500W power rating, so you will probably loose a bit of SPL to power compression. The 810 will experience less power compression because it is running at < half of rated power.