Any cab potential loudness measurement formula for SPL/Displacement?
Just wondering. Or are there just too many other variables to make a determination (especially, perhaps, taking into consideration the frequency response chart)? If this is the answer, no worries, will be a very short thread :D . Or is the only way to know to build them & measure real-world sonic results?
For instance (although could be any drivers you might choose), a 4 ohm 212 w/Faital Pro 12PR300s (no additional drivers) vs. a 4 ohm 215 w/Eminence Alpha 15-As (also no additional drivers). Both cabs built by the same builder with equal care & attention to driver/cab specs. Both cabs driven by the same amp, let's say a Streamliner 900 (900 watts @ 4 ohms).
This 212 would be a 600 watt RMS box. SPL would be ~102. Vd ~517mm. Frequency response 50Hz-5kHz.
This 215 would be a 400 watt RMS cab. SPL would be ~100. Vd ~650. Frequency response 46Hz-3.5kHz.
Design software will get you pretty close, but real world would need to be measured with the actual drivers in their enclosures. The potential loudness can be found in the input power to SPL/displacement charts. Look for the maximum input power to displacement limited SPL. It will be much higher that the 1W/M figure you quoted.
I don't know the actual mathematical formula for calculating excursion, I let WinISD do it for me.:D
The max. power chart will tell you how many watts it takes to reach xmax. You can up the power and find out where it reaches xlim.
As for broadband spl....double power = 3db and ten times power = 10db.
So, disregarding frequency response for a minute and using an average spl figure....lets say your driver is rated 97db @ 1 watt. Doubling driver count gets you 3db so your 2x cab would be an average of 100db @ 1 watt.....so that means 110db at 10 watts.....120db at 100 watts and 123db at 200 watts. I stop counting at 200 watts, beyond that, it takes a whole lot more power for very little additional output. For example, you'd need 1000 watts to reach 130db and this is beyond what most drivers can handle. Vd, xmax, etc. dictate output in the low frequencies.
Somewhere up there, there is some physics thing where the system can't be made to go louder no matter how much power you throw at it.
Those numbers are for a measurement 1 meter away from the cab. Ignoring room effects (like playing outdoors/measuring in 1/2 space) you lose 6db for every doubling of distance away from the source. So....if you're at 123db @ 1 meter, you get 117 db 2 meters away, like on stage 6 feet from the rig, 111 db 4 meters away, like the dancefloor in a small club, 105 db 8 meters away like the nearer audience in that small club, and 99db 16 meters away like the folks further toward the back in that same club.
Those are raw numbers for figuring output, of course, room effects, frequency cancellations, eqing, bodies soaking up sound, etc. all come into play and you're likely not up in the high 90's-100 db in there or you'd get asked to turn down.:p
Should note that all those numbers are figured for a sine wave input, which a vibrating string is not. 100 watts of sinewave would cause pain. Sending a vibrating string through a 100 watt amp and those speakers isn't nearly as loud. There is a spike in power demand in the first few milliseconds as you strike the note and much less as the note plays out, so of those 100 watts, you might be hearing 30 of them as the note rings. That all happens so fast, no human can play fast enough to keep the power demand up where it is in those first few milliseconds of note attack.
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