I do believe that I answered all of his questions within my post. To make it perhaps clearer: the volume level between the two cabs running either way will be almost identical.
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I do believe that I answered all of his questions within my post. To make it perhaps clearer: the volume level between the two cabs running either way will be almost identical.
But there is no point in not running them together!
OK It looks like I missunderstood what the OP is asking.
If you have two amps (one hooked to each speaker), you can probably make the whole rig balance decently, although the hassle factor of doing that is high. Although the 4 ohm cabinet will get more power, the difference in acoustic output isn't that huge even if the amp you're using doubles its output into the lower nominal impedance (very few amps can actually do that). The biggest advantage of running two cabinets together is that you'll get some coupling at low frequencies that'll make it sound bigger and make it seem that it goes lower.
Another thing to consider is that many 4 ohm speakers have lower
sensitivity than the 8 ohm version of the same speaker.
That will cancel out some of the gain from the extra power.
After several different amps and cabs, I eventually got an amp and cab that
could put out more than I really needed at 8 ohms.
That lets me have plaenty of headroom, without working the amp or
cab and have the option of adding a second cab to double speaker area
and halve inpedence...
just in case I ever need to cause earthquakes or play festivals without PA support.
sensitivity than the 8 ohm version of the same speaker.
That will cancel out some of the gain from the extra power.
After several different amps and cabs, I eventually got an amp and cab that
could put out more than I really needed at 8 ohms.
That lets me have plaenty of headroom, without working the amp or
cab and have the option of adding a second cab to double speaker area
and halve inpedence...
just in case I ever need to cause earthquakes or play festivals without PA support.
This. OP this seems like the best solution so far, IMO. One cab and amp that you like the sound of, that has an 8 ohm max output higher than you will likely need. 8 ohm cab. Done for the foreseeable future.
If the cab impedence was the only variable you could say that the amp would probably deliver more power to the 4-ohm cab than to the 8-ohm cab. There are other variables in the analysis, which there's no point in exploring outside an engineering meeting. You would find that the 4-ohm cab is likely, though not certainly, going to be discernibly louder but not impressively louder than the 8 when using the same amp. So, how about swapping for a bigger amp head? In swapping the 8-ohm cab from one amp to a more powerful amp, let's say doubling the amp's rated power, you will hear that the cab's output increases discernibly but still not greatly. It may match the sound pressure level of the 4-ohm cab but I'd keep my expectations in check because it's more academic than useful. Then, again, people do win the lottos.
To the OP I would say that if everything else is equal then yes, you can get a sound level from an 8 Ohm cab and amp equal to the sound level that you can get from a 4 Ohm cab and a different amp. In fact, even if things are not all equal you can still do this, you just need to deal with more devilish details correctly.
If you design the system correctly then you can deliver any desired amount of power to any load impedance. The power delivered to a resistive load is V*V/R, where V is the rms voltage of the signal and R is the load resistance. In an electronic amplifer the maximum possible output V is ultimately set by the amplifier's power supply voltage. The two are not equal of course but the maximum possible signal rms voltage at an acceptable distortion level will be some fraction of the power supply's voltage. If you want 500 W into 4 Ohms then V must be about 45 V. If you want 500 W into 8 Ohms then V must be about 63 V. If you want 500 W into the common radio system impedance of 50 Ohms then V must be 158 V but in a radio system impedance matching can be used to allow the amplifier output to see a lower impedance than the antenna actually presents and that changes the game as far as the power supply is concerned. But the transmission line to the antenna and the antenna itself must be designed to handle 158 Vrms.
But the bottom line is that if you have two cabs with equal efficiency and you connect the 4 Ohm cab to an amp that is rated at 500 W into 4 Ohms it will sound equally loud as an 8 Ohm cab connected to an amp that is rated at 500 W into 8 Ohms. If the two cabs differ in efficiency or some other factor that affects the perceived loudness versus power curve then you will need to adjust the two amplifier output power ratings accordingly to equalize the loudness.
If you design the system correctly then you can deliver any desired amount of power to any load impedance. The power delivered to a resistive load is V*V/R, where V is the rms voltage of the signal and R is the load resistance. In an electronic amplifer the maximum possible output V is ultimately set by the amplifier's power supply voltage. The two are not equal of course but the maximum possible signal rms voltage at an acceptable distortion level will be some fraction of the power supply's voltage. If you want 500 W into 4 Ohms then V must be about 45 V. If you want 500 W into 8 Ohms then V must be about 63 V. If you want 500 W into the common radio system impedance of 50 Ohms then V must be 158 V but in a radio system impedance matching can be used to allow the amplifier output to see a lower impedance than the antenna actually presents and that changes the game as far as the power supply is concerned. But the transmission line to the antenna and the antenna itself must be designed to handle 158 Vrms.
But the bottom line is that if you have two cabs with equal efficiency and you connect the 4 Ohm cab to an amp that is rated at 500 W into 4 Ohms it will sound equally loud as an 8 Ohm cab connected to an amp that is rated at 500 W into 8 Ohms. If the two cabs differ in efficiency or some other factor that affects the perceived loudness versus power curve then you will need to adjust the two amplifier output power ratings accordingly to equalize the loudness.
